Finite Math Examples

Solve in Terms of the Arbitrary Variable y 2x+2y-z=7 , x-3y+z=24
,
Step 1
Solve the equation for .
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Step 1.1
Move all terms not containing to the right side of the equation.
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Step 1.1.1
Subtract from both sides of the equation.
Step 1.1.2
Add to 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
Cancel the common factor of and .
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Step 1.2.3.1.1
Factor out of .
Step 1.2.3.1.2
Cancel the common factors.
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Step 1.2.3.1.2.1
Factor out of .
Step 1.2.3.1.2.2
Cancel the common factor.
Step 1.2.3.1.2.3
Rewrite the expression.
Step 1.2.3.1.2.4
Divide by .
Step 2
Solve the equation for .
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Step 2.1
Simplify .
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Step 2.1.1
Subtract from .
Step 2.1.2
To write as a fraction with a common denominator, multiply by .
Step 2.1.3
Simplify terms.
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Step 2.1.3.1
Combine and .
Step 2.1.3.2
Combine the numerators over the common denominator.
Step 2.1.3.3
Combine the numerators over the common denominator.
Step 2.1.4
Move to the left of .
Step 2.1.5
Add and .
Step 2.1.6
To write as a fraction with a common denominator, multiply by .
Step 2.1.7
Combine and .
Step 2.1.8
Combine the numerators over the common denominator.
Step 2.1.9
Multiply by .
Step 2.1.10
Factor out of .
Step 2.1.11
Rewrite as .
Step 2.1.12
Factor out of .
Step 2.1.13
Factor out of .
Step 2.1.14
Factor out of .
Step 2.1.15
Simplify the expression.
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Step 2.1.15.1
Rewrite as .
Step 2.1.15.2
Move the negative in front of the fraction.
Step 2.2
Multiply both sides of the equation by .
Step 2.3
Simplify both sides of the equation.
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Step 2.3.1
Simplify the left side.
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Step 2.3.1.1
Simplify .
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Step 2.3.1.1.1
Cancel the common factor of .
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Step 2.3.1.1.1.1
Move the leading negative in into the numerator.
Step 2.3.1.1.1.2
Factor out of .
Step 2.3.1.1.1.3
Cancel the common factor.
Step 2.3.1.1.1.4
Rewrite the expression.
Step 2.3.1.1.2
Multiply.
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Step 2.3.1.1.2.1
Multiply by .
Step 2.3.1.1.2.2
Multiply by .
Step 2.3.2
Simplify the right side.
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Step 2.3.2.1
Multiply by .
Step 2.4
Move all terms not containing to the right side of the equation.
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Step 2.4.1
Subtract from both sides of the equation.
Step 2.4.2
Add to both sides of the equation.
Step 2.4.3
Add and .
Step 2.5
Divide each term in by and simplify.
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Step 2.5.1
Divide each term in by .
Step 2.5.2
Simplify the left side.
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Step 2.5.2.1
Cancel the common factor of .
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Step 2.5.2.1.1
Cancel the common factor.
Step 2.5.2.1.2
Divide by .
Step 2.5.3
Simplify the right side.
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Step 2.5.3.1
Simplify each term.
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Step 2.5.3.1.1
Dividing two negative values results in a positive value.
Step 2.5.3.1.2
Dividing two negative values results in a positive value.
Step 3
Simplify the right side.
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Step 3.1
Simplify .
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Step 3.1.1
Combine the numerators over the common denominator.
Step 3.1.2
To write as a fraction with a common denominator, multiply by .
Step 3.1.3
Combine and .
Step 3.1.4
Combine the numerators over the common denominator.
Step 3.1.5
Simplify the numerator.
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Step 3.1.5.1
Multiply by .
Step 3.1.5.2
Add and .
Step 3.1.6
Simplify each term.
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Step 3.1.6.1
Simplify the numerator.
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Step 3.1.6.1.1
Combine the numerators over the common denominator.
Step 3.1.6.1.2
Factor out of .
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Step 3.1.6.1.2.1
Factor out of .
Step 3.1.6.1.2.2
Factor out of .
Step 3.1.6.1.2.3
Factor out of .
Step 3.1.6.2
Multiply the numerator by the reciprocal of the denominator.
Step 3.1.6.3
Cancel the common factor of .
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Step 3.1.6.3.1
Cancel the common factor.
Step 3.1.6.3.2
Rewrite the expression.
Step 3.1.7
To write as a fraction with a common denominator, multiply by .
Step 3.1.8
Simplify terms.
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Step 3.1.8.1
Combine and .
Step 3.1.8.2
Combine the numerators over the common denominator.
Step 3.1.9
Simplify the numerator.
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Step 3.1.9.1
Multiply by .
Step 3.1.9.2
Add and .