Finite Math Examples

Solve by Substitution y=-1/2x+5 , y=3x-2
,
Step 1
Eliminate the equal sides of each equation and combine.
Step 2
Solve for .
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Step 2.1
Combine and .
Step 2.2
Move all terms containing to the left side of the equation.
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Step 2.2.1
Subtract from both sides of the equation.
Step 2.2.2
To write as a fraction with a common denominator, multiply by .
Step 2.2.3
Combine and .
Step 2.2.4
Combine the numerators over the common denominator.
Step 2.2.5
Simplify each term.
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Step 2.2.5.1
Simplify the numerator.
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Step 2.2.5.1.1
Factor out of .
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Step 2.2.5.1.1.1
Factor out of .
Step 2.2.5.1.1.2
Factor out of .
Step 2.2.5.1.1.3
Factor out of .
Step 2.2.5.1.2
Multiply by .
Step 2.2.5.1.3
Subtract from .
Step 2.2.5.2
Move to the left of .
Step 2.2.5.3
Move the negative in front of the fraction.
Step 2.3
Move all terms not containing to the right side of the equation.
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Step 2.3.1
Subtract from both sides of the equation.
Step 2.3.2
Subtract from .
Step 2.4
Multiply both sides of the equation by .
Step 2.5
Simplify both sides of the equation.
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Step 2.5.1
Simplify the left side.
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Step 2.5.1.1
Simplify .
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Step 2.5.1.1.1
Cancel the common factor of .
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Step 2.5.1.1.1.1
Move the leading negative in into the numerator.
Step 2.5.1.1.1.2
Move the leading negative in into the numerator.
Step 2.5.1.1.1.3
Factor out of .
Step 2.5.1.1.1.4
Cancel the common factor.
Step 2.5.1.1.1.5
Rewrite the expression.
Step 2.5.1.1.2
Cancel the common factor of .
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Step 2.5.1.1.2.1
Factor out of .
Step 2.5.1.1.2.2
Cancel the common factor.
Step 2.5.1.1.2.3
Rewrite the expression.
Step 2.5.1.1.3
Multiply.
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Step 2.5.1.1.3.1
Multiply by .
Step 2.5.1.1.3.2
Multiply by .
Step 2.5.2
Simplify the right side.
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Step 2.5.2.1
Simplify .
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Step 2.5.2.1.1
Cancel the common factor of .
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Step 2.5.2.1.1.1
Move the leading negative in into the numerator.
Step 2.5.2.1.1.2
Factor out of .
Step 2.5.2.1.1.3
Cancel the common factor.
Step 2.5.2.1.1.4
Rewrite the expression.
Step 2.5.2.1.2
Multiply by .
Step 3
Evaluate when .
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Step 3.1
Substitute for .
Step 3.2
Simplify .
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Step 3.2.1
Multiply by .
Step 3.2.2
Subtract from .
Step 4
The solution to the system is the complete set of ordered pairs that are valid solutions.
Step 5
The result can be shown in multiple forms.
Point Form:
Equation Form:
Step 6