Finite Math Examples

Solve by Substitution 40a+60b=32000 , 1.5a+2b=60000
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Step 1
Solve for in .
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Step 1.1
Subtract from both sides of the equation.
Step 1.2
Divide each term in by and simplify.
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Step 1.2.1
Divide each term in by .
Step 1.2.2
Simplify the left side.
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Step 1.2.2.1
Cancel the common factor of .
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Step 1.2.2.1.1
Cancel the common factor.
Step 1.2.2.1.2
Divide by .
Step 1.2.3
Simplify the right side.
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Step 1.2.3.1
Simplify each term.
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Step 1.2.3.1.1
Divide by .
Step 1.2.3.1.2
Cancel the common factor of and .
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Step 1.2.3.1.2.1
Factor out of .
Step 1.2.3.1.2.2
Cancel the common factors.
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Step 1.2.3.1.2.2.1
Factor out of .
Step 1.2.3.1.2.2.2
Cancel the common factor.
Step 1.2.3.1.2.2.3
Rewrite the expression.
Step 1.2.3.1.3
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
Apply the distributive property.
Step 2.2.1.1.2
Multiply by .
Step 2.2.1.1.3
Multiply .
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Step 2.2.1.1.3.1
Multiply by .
Step 2.2.1.1.3.2
Combine and .
Step 2.2.1.1.3.3
Multiply by .
Step 2.2.1.1.4
Simplify each term.
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Step 2.2.1.1.4.1
Move the negative in front of the fraction.
Step 2.2.1.1.4.2
Factor out of .
Step 2.2.1.1.4.3
Factor out of .
Step 2.2.1.1.4.4
Separate fractions.
Step 2.2.1.1.4.5
Divide by .
Step 2.2.1.1.4.6
Divide by .
Step 2.2.1.1.4.7
Multiply by .
Step 2.2.1.2
Add and .
Step 3
Solve for in .
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Step 3.1
Move all terms not containing to the right side of the equation.
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Step 3.1.1
Subtract from both sides of the equation.
Step 3.1.2
Subtract from .
Step 3.2
Divide each term in by and simplify.
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Step 3.2.1
Divide each term in by .
Step 3.2.2
Simplify the left side.
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Step 3.2.2.1
Cancel the common factor of .
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Step 3.2.2.1.1
Cancel the common factor.
Step 3.2.2.1.2
Divide by .
Step 3.2.3
Simplify the right side.
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Step 3.2.3.1
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
Simplify each term.
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Step 4.2.1.1.1
Cancel the common factor of and .
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Step 4.2.1.1.1.1
Factor out of .
Step 4.2.1.1.1.2
Cancel the common factors.
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Step 4.2.1.1.1.2.1
Factor out of .
Step 4.2.1.1.1.2.2
Cancel the common factor.
Step 4.2.1.1.1.2.3
Rewrite the expression.
Step 4.2.1.1.1.2.4
Divide by .
Step 4.2.1.1.2
Multiply .
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Step 4.2.1.1.2.1
Multiply by .
Step 4.2.1.1.2.2
Multiply by .
Step 4.2.1.2
Add and .
Step 5
List all of the solutions.