Finite Math Examples

Solve in Terms of the Arbitrary Variable k 2x-y=5 , 4x+ky=9
,
Step 1
Solve the equation for .
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Step 1.1
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 2
Solve the equation for .
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Step 2.1
Simplify each term.
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Step 2.1.1
Apply the distributive property.
Step 2.1.2
Cancel the common factor of .
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Step 2.1.2.1
Factor out of .
Step 2.1.2.2
Cancel the common factor.
Step 2.1.2.3
Rewrite the expression.
Step 2.1.3
Multiply by .
Step 2.1.4
Cancel the common factor of .
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Step 2.1.4.1
Factor out of .
Step 2.1.4.2
Cancel the common factor.
Step 2.1.4.3
Rewrite the expression.
Step 2.2
Move all terms not containing to the right side of the equation.
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Step 2.2.1
Subtract from both sides of the equation.
Step 2.2.2
Subtract from .
Step 2.3
Factor out of .
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Step 2.3.1
Factor out of .
Step 2.3.2
Factor out of .
Step 2.3.3
Factor out of .
Step 2.3.4
Multiply by .
Step 2.4
Divide each term in by and simplify.
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Step 2.4.1
Divide each term in by .
Step 2.4.2
Simplify the left side.
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Step 2.4.2.1
Cancel the common factor of .
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Step 2.4.2.1.1
Cancel the common factor.
Step 2.4.2.1.2
Divide by .
Step 2.4.3
Simplify the right side.
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Step 2.4.3.1
Move the negative in front of the fraction.
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
Simplify terms.
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Step 3.1.3.1
Combine and .
Step 3.1.3.2
Combine the numerators over the common denominator.
Step 3.1.4
Simplify the numerator.
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Step 3.1.4.1
Apply the distributive property.
Step 3.1.4.2
Multiply by .
Step 3.1.4.3
Subtract from .
Step 3.1.5
Multiply the numerator by the reciprocal of the denominator.
Step 3.1.6
Multiply by .
Step 3.1.7
Move to the left of .