Finite Math Examples

Solve by Substitution 5(4x+y)-(x-3y)=-5 , 2(x-2y)+(2x-y)=19
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Step 1
Solve for in .
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Step 1.1
Simplify .
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Step 1.1.1
Simplify each term.
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Step 1.1.1.1
Apply the distributive property.
Step 1.1.1.2
Multiply by .
Step 1.1.2
Simplify by adding terms.
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Step 1.1.2.1
Subtract from .
Step 1.1.2.2
Add and .
Step 1.2
Subtract from both sides of the equation.
Step 1.3
Divide each term in by and simplify.
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Step 1.3.1
Divide each term in by .
Step 1.3.2
Simplify the left side.
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Step 1.3.2.1
Cancel the common factor of .
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Step 1.3.2.1.1
Cancel the common factor.
Step 1.3.2.1.2
Divide by .
Step 1.3.3
Simplify the right side.
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Step 1.3.3.1
Simplify each term.
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Step 1.3.3.1.1
Move the negative in front of the fraction.
Step 1.3.3.1.2
Move the negative in front of the fraction.
Step 2
Replace all occurrences of with in each equation.
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Step 2.1
Replace all occurrences of in with .
Step 2.2
Simplify the left side.
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Step 2.2.1
Simplify .
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Step 2.2.1.1
Simplify each term.
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Step 2.2.1.1.1
To write as a fraction with a common denominator, multiply by .
Step 2.2.1.1.2
Combine and .
Step 2.2.1.1.3
Combine the numerators over the common denominator.
Step 2.2.1.1.4
Combine the numerators over the common denominator.
Step 2.2.1.1.5
Multiply by .
Step 2.2.1.1.6
Subtract from .
Step 2.2.1.1.7
Combine and .
Step 2.2.1.1.8
Apply the distributive property.
Step 2.2.1.1.9
Multiply .
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Step 2.2.1.1.9.1
Multiply by .
Step 2.2.1.1.9.2
Combine and .
Step 2.2.1.1.9.3
Multiply by .
Step 2.2.1.1.10
Multiply .
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Step 2.2.1.1.10.1
Multiply by .
Step 2.2.1.1.10.2
Combine and .
Step 2.2.1.1.10.3
Multiply by .
Step 2.2.1.1.11
Simplify each term.
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Step 2.2.1.1.11.1
Move the negative in front of the fraction.
Step 2.2.1.1.11.2
Move the negative in front of the fraction.
Step 2.2.1.2
Combine the numerators over the common denominator.
Step 2.2.1.3
Simplify each term.
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Step 2.2.1.3.1
Apply the distributive property.
Step 2.2.1.3.2
Multiply by .
Step 2.2.1.3.3
Multiply by .
Step 2.2.1.4
Simplify terms.
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Step 2.2.1.4.1
Subtract from .
Step 2.2.1.4.2
Subtract from .
Step 2.2.1.4.3
Factor out of .
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Step 2.2.1.4.3.1
Factor out of .
Step 2.2.1.4.3.2
Factor out of .
Step 2.2.1.4.3.3
Factor out of .
Step 2.2.1.5
To write as a fraction with a common denominator, multiply by .
Step 2.2.1.6
Simplify terms.
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Step 2.2.1.6.1
Combine and .
Step 2.2.1.6.2
Combine the numerators over the common denominator.
Step 2.2.1.7
Simplify the numerator.
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Step 2.2.1.7.1
Multiply by .
Step 2.2.1.7.2
Apply the distributive property.
Step 2.2.1.7.3
Multiply by .
Step 2.2.1.7.4
Multiply by .
Step 2.2.1.7.5
Subtract from .
Step 2.2.1.8
Simplify with factoring out.
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Step 2.2.1.8.1
Factor out of .
Step 2.2.1.8.2
Rewrite as .
Step 2.2.1.8.3
Factor out of .
Step 2.2.1.8.4
Simplify the expression.
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Step 2.2.1.8.4.1
Rewrite as .
Step 2.2.1.8.4.2
Move the negative in front of the fraction.
Step 3
Solve for in .
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Step 3.1
Multiply both sides of the equation by .
Step 3.2
Simplify both sides of the equation.
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Step 3.2.1
Simplify the left side.
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Step 3.2.1.1
Simplify .
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Step 3.2.1.1.1
Cancel the common factor of .
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Step 3.2.1.1.1.1
Move the leading negative in into the numerator.
Step 3.2.1.1.1.2
Factor out of .
Step 3.2.1.1.1.3
Cancel the common factor.
Step 3.2.1.1.1.4
Rewrite the expression.
Step 3.2.1.1.2
Multiply.
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Step 3.2.1.1.2.1
Multiply by .
Step 3.2.1.1.2.2
Multiply by .
Step 3.2.2
Simplify the right side.
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Step 3.2.2.1
Multiply by .
Step 3.3
Move all terms not containing to the right side of the equation.
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Step 3.3.1
Subtract from both sides of the equation.
Step 3.3.2
Subtract from .
Step 3.4
Divide each term in by and simplify.
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Step 3.4.1
Divide each term in by .
Step 3.4.2
Simplify the left side.
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Step 3.4.2.1
Cancel the common factor of .
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Step 3.4.2.1.1
Cancel the common factor.
Step 3.4.2.1.2
Divide by .
Step 3.4.3
Simplify the right side.
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Step 3.4.3.1
Divide by .
Step 4
Replace all occurrences of with in each equation.
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Step 4.1
Replace all occurrences of in with .
Step 4.2
Simplify the right side.
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Step 4.2.1
Simplify .
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Step 4.2.1.1
Combine the numerators over the common denominator.
Step 4.2.1.2
Simplify the expression.
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Step 4.2.1.2.1
Multiply by .
Step 4.2.1.2.2
Add and .
Step 4.2.1.2.3
Divide by .
Step 5
The solution to the system is the complete set of ordered pairs that are valid solutions.
Step 6
The result can be shown in multiple forms.
Point Form:
Equation Form:
Step 7