Finite Math Examples

Solve by Substitution 35x+70y+175d+70w=2240 , 40x+40y+80d+70w=1120 , 40x+30y+70d+10w=920 , w=1
, , ,
Step 1
Replace all occurrences of with in each equation.
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Step 1.1
Replace all occurrences of in with .
Step 1.2
Simplify the left side.
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Step 1.2.1
Multiply by .
Step 1.3
Replace all occurrences of in with .
Step 1.4
Simplify the left side.
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Step 1.4.1
Multiply by .
Step 1.5
Replace all occurrences of in with .
Step 1.6
Simplify the left side.
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Step 1.6.1
Multiply by .
Step 2
Solve for in .
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Step 2.1
Move all terms not containing to the right side of the equation.
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Step 2.1.1
Subtract from both sides of the equation.
Step 2.1.2
Subtract from both sides of the equation.
Step 2.1.3
Subtract from both sides of the equation.
Step 2.1.4
Subtract from .
Step 2.2
Divide each term in by and simplify.
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Step 2.2.1
Divide each term in by .
Step 2.2.2
Simplify the left side.
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Step 2.2.2.1
Cancel the common factor of .
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Step 2.2.2.1.1
Cancel the common factor.
Step 2.2.2.1.2
Divide by .
Step 2.2.3
Simplify the right side.
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Step 2.2.3.1
Simplify each term.
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Step 2.2.3.1.1
Cancel the common factor of and .
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Step 2.2.3.1.1.1
Factor out of .
Step 2.2.3.1.1.2
Cancel the common factors.
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Step 2.2.3.1.1.2.1
Factor out of .
Step 2.2.3.1.1.2.2
Cancel the common factor.
Step 2.2.3.1.1.2.3
Rewrite the expression.
Step 2.2.3.1.2
Move the negative in front of the fraction.
Step 2.2.3.1.3
Cancel the common factor of and .
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Step 2.2.3.1.3.1
Factor out of .
Step 2.2.3.1.3.2
Cancel the common factors.
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Step 2.2.3.1.3.2.1
Factor out of .
Step 2.2.3.1.3.2.2
Cancel the common factor.
Step 2.2.3.1.3.2.3
Rewrite the expression.
Step 2.2.3.1.4
Move the negative in front of the fraction.
Step 2.2.3.1.5
Cancel the common factor of and .
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Step 2.2.3.1.5.1
Factor out of .
Step 2.2.3.1.5.2
Cancel the common factors.
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Step 2.2.3.1.5.2.1
Factor out of .
Step 2.2.3.1.5.2.2
Cancel the common factor.
Step 2.2.3.1.5.2.3
Rewrite the expression.
Step 3
Replace all occurrences of with in each equation.
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Step 3.1
Replace all occurrences of in with .
Step 3.2
Simplify the left side.
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Step 3.2.1
Simplify .
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Step 3.2.1.1
Simplify each term.
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Step 3.2.1.1.1
Apply the distributive property.
Step 3.2.1.1.2
Simplify.
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Step 3.2.1.1.2.1
Cancel the common factor of .
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Step 3.2.1.1.2.1.1
Move the leading negative in into the numerator.
Step 3.2.1.1.2.1.2
Factor out of .
Step 3.2.1.1.2.1.3
Cancel the common factor.
Step 3.2.1.1.2.1.4
Rewrite the expression.
Step 3.2.1.1.2.2
Multiply by .
Step 3.2.1.1.2.3
Cancel the common factor of .
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Step 3.2.1.1.2.3.1
Move the leading negative in into the numerator.
Step 3.2.1.1.2.3.2
Factor out of .
Step 3.2.1.1.2.3.3
Cancel the common factor.
Step 3.2.1.1.2.3.4
Rewrite the expression.
Step 3.2.1.1.2.4
Multiply by .
Step 3.2.1.1.2.5
Cancel the common factor of .
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Step 3.2.1.1.2.5.1
Factor out of .
Step 3.2.1.1.2.5.2
Cancel the common factor.
Step 3.2.1.1.2.5.3
Rewrite the expression.
Step 3.2.1.1.2.6
Multiply by .
Step 3.2.1.2
Simplify by adding terms.
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Step 3.2.1.2.1
Add and .
Step 3.2.1.2.2
Add and .
Step 3.2.1.2.3
Add and .
Step 3.3
Replace all occurrences of in with .
Step 3.4
Simplify the left side.
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Step 3.4.1
Simplify .
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Step 3.4.1.1
Simplify each term.
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Step 3.4.1.1.1
Apply the distributive property.
Step 3.4.1.1.2
Simplify.
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Step 3.4.1.1.2.1
Multiply .
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Step 3.4.1.1.2.1.1
Multiply by .
Step 3.4.1.1.2.1.2
Combine and .
Step 3.4.1.1.2.1.3
Multiply by .
Step 3.4.1.1.2.2
Multiply .
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Step 3.4.1.1.2.2.1
Multiply by .
Step 3.4.1.1.2.2.2
Combine and .
Step 3.4.1.1.2.2.3
Multiply by .
Step 3.4.1.1.2.3
Multiply .
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Step 3.4.1.1.2.3.1
Combine and .
Step 3.4.1.1.2.3.2
Multiply by .
Step 3.4.1.1.3
Simplify each term.
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Step 3.4.1.1.3.1
Move the negative in front of the fraction.
Step 3.4.1.1.3.2
Move the negative in front of the fraction.
Step 3.4.1.2
To write as a fraction with a common denominator, multiply by .
Step 3.4.1.3
Combine and .
Step 3.4.1.4
Combine the numerators over the common denominator.
Step 3.4.1.5
Combine the numerators over the common denominator.
Step 3.4.1.6
Multiply by .
Step 3.4.1.7
Add and .
Step 3.4.1.8
Factor out of .
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Step 3.4.1.8.1
Factor out of .
Step 3.4.1.8.2
Factor out of .
Step 3.4.1.8.3
Factor out of .
Step 3.4.1.8.4
Factor out of .
Step 3.4.1.8.5
Factor out of .
Step 3.4.1.9
To write as a fraction with a common denominator, multiply by .
Step 3.4.1.10
Simplify terms.
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Step 3.4.1.10.1
Combine and .
Step 3.4.1.10.2
Combine the numerators over the common denominator.
Step 3.4.1.11
Simplify the numerator.
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Step 3.4.1.11.1
Factor out of .
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Step 3.4.1.11.1.1
Factor out of .
Step 3.4.1.11.1.2
Factor out of .
Step 3.4.1.11.2
Multiply by .
Step 3.4.1.11.3
Subtract from .
Step 3.4.1.12
To write as a fraction with a common denominator, multiply by .
Step 3.4.1.13
Simplify terms.
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Step 3.4.1.13.1
Combine and .
Step 3.4.1.13.2
Combine the numerators over the common denominator.
Step 3.4.1.14
Simplify the numerator.
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Step 3.4.1.14.1
Factor out of .
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Step 3.4.1.14.1.1
Factor out of .
Step 3.4.1.14.1.2
Factor out of .
Step 3.4.1.14.2
Multiply by .
Step 3.4.1.14.3
Add and .
Step 4
Solve for in .
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Step 4.1
Move all terms not containing to the right side of the equation.
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Step 4.1.1
Subtract from both sides of the equation.
Step 4.1.2
Subtract from both sides of the equation.
Step 4.1.3
Subtract from .
Step 4.2
Divide each term in by and simplify.
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Step 4.2.1
Divide each term in by .
Step 4.2.2
Simplify the left side.
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Step 4.2.2.1
Cancel the common factor of .
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Step 4.2.2.1.1
Cancel the common factor.
Step 4.2.2.1.2
Divide by .
Step 4.2.3
Simplify the right side.
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Step 4.2.3.1
Simplify each term.
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Step 4.2.3.1.1
Cancel the common factor of and .
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Step 4.2.3.1.1.1
Factor out of .
Step 4.2.3.1.1.2
Cancel the common factors.
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Step 4.2.3.1.1.2.1
Factor out of .
Step 4.2.3.1.1.2.2
Cancel the common factor.
Step 4.2.3.1.1.2.3
Rewrite the expression.
Step 4.2.3.1.1.2.4
Divide by .
Step 4.2.3.1.2
Divide by .
Step 5
Replace all occurrences of with in each equation.
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Step 5.1
Replace all occurrences of in with .
Step 5.2
Simplify the left side.
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Step 5.2.1
Simplify the numerator.
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Step 5.2.1.1
Apply the distributive property.
Step 5.2.1.2
Multiply by .
Step 5.2.1.3
Multiply by .
Step 5.2.1.4
Subtract from .
Step 5.2.1.5
Add and .
Step 5.3
Replace all occurrences of in with .
Step 5.4
Simplify the right side.
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Step 5.4.1
Simplify .
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Step 5.4.1.1
Combine the numerators over the common denominator.
Step 5.4.1.2
Simplify each term.
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Step 5.4.1.2.1
Apply the distributive property.
Step 5.4.1.2.2
Multiply by .
Step 5.4.1.2.3
Multiply by .
Step 5.4.1.3
Simplify terms.
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Step 5.4.1.3.1
Subtract from .
Step 5.4.1.3.2
Add and .
Step 5.4.1.3.3
Factor out of .
Step 5.4.1.3.4
Rewrite as .
Step 5.4.1.3.5
Factor out of .
Step 5.4.1.3.6
Simplify the expression.
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Step 5.4.1.3.6.1
Rewrite as .
Step 5.4.1.3.6.2
Move the negative in front of the fraction.
Step 6
Solve for in .
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Step 6.1
Multiply both sides by .
Step 6.2
Simplify.
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Step 6.2.1
Simplify the left side.
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Step 6.2.1.1
Simplify .
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Step 6.2.1.1.1
Cancel the common factor of .
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Step 6.2.1.1.1.1
Cancel the common factor.
Step 6.2.1.1.1.2
Rewrite the expression.
Step 6.2.1.1.2
Apply the distributive property.
Step 6.2.1.1.3
Multiply.
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Step 6.2.1.1.3.1
Multiply by .
Step 6.2.1.1.3.2
Multiply by .
Step 6.2.2
Simplify the right side.
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Step 6.2.2.1
Multiply by .
Step 6.3
Solve for .
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Step 6.3.1
Move all terms not containing to the right side of the equation.
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Step 6.3.1.1
Subtract from both sides of the equation.
Step 6.3.1.2
Subtract from .
Step 6.3.2
Divide each term in by and simplify.
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Step 6.3.2.1
Divide each term in by .
Step 6.3.2.2
Simplify the left side.
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Step 6.3.2.2.1
Cancel the common factor of .
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Step 6.3.2.2.1.1
Cancel the common factor.
Step 6.3.2.2.1.2
Divide by .
Step 6.3.2.3
Simplify the right side.
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Step 6.3.2.3.1
Cancel the common factor of and .
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Step 6.3.2.3.1.1
Factor out of .
Step 6.3.2.3.1.2
Cancel the common factors.
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Step 6.3.2.3.1.2.1
Factor out of .
Step 6.3.2.3.1.2.2
Cancel the common factor.
Step 6.3.2.3.1.2.3
Rewrite the expression.
Step 7
Replace all occurrences of with in each equation.
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Step 7.1
Replace all occurrences of in with .
Step 7.2
Simplify the right side.
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Step 7.2.1
Simplify .
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Step 7.2.1.1
Simplify the numerator.
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Step 7.2.1.1.1
Cancel the common factor of .
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Step 7.2.1.1.1.1
Factor out of .
Step 7.2.1.1.1.2
Cancel the common factor.
Step 7.2.1.1.1.3
Rewrite the expression.
Step 7.2.1.1.2
To write as a fraction with a common denominator, multiply by .
Step 7.2.1.1.3
Combine and .
Step 7.2.1.1.4
Combine the numerators over the common denominator.
Step 7.2.1.1.5
Simplify the numerator.
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Step 7.2.1.1.5.1
Multiply by .
Step 7.2.1.1.5.2
Subtract from .
Step 7.2.1.1.6
Move the negative in front of the fraction.
Step 7.2.1.2
Multiply the numerator by the reciprocal of the denominator.
Step 7.2.1.3
Multiply .
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Step 7.2.1.3.1
Multiply by .
Step 7.2.1.3.2
Multiply by .
Step 7.2.1.4
Multiply .
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Step 7.2.1.4.1
Multiply by .
Step 7.2.1.4.2
Multiply by .
Step 7.3
Replace all occurrences of in with .
Step 7.4
Simplify the right side.
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Step 7.4.1
Simplify .
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Step 7.4.1.1
To write as a fraction with a common denominator, multiply by .
Step 7.4.1.2
Combine and .
Step 7.4.1.3
Combine the numerators over the common denominator.
Step 7.4.1.4
Simplify the numerator.
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Step 7.4.1.4.1
Multiply by .
Step 7.4.1.4.2
Add and .
Step 8
List all of the solutions.