Finite Math Examples

Solve by Substitution y=3/2x-1/2 , y=-2x+24
,
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
Add to 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
Combine the numerators over the common denominator.
Step 2.2.6
Multiply by .
Step 2.2.7
Add and .
Step 2.3
Multiply both sides by .
Step 2.4
Simplify.
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Step 2.4.1
Simplify the left side.
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Step 2.4.1.1
Cancel the common factor of .
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Step 2.4.1.1.1
Cancel the common factor.
Step 2.4.1.1.2
Rewrite the expression.
Step 2.4.2
Simplify the right side.
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Step 2.4.2.1
Multiply by .
Step 2.5
Solve for .
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Step 2.5.1
Move all terms not containing to the right side of the equation.
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Step 2.5.1.1
Add to both sides of the equation.
Step 2.5.1.2
Add and .
Step 2.5.2
Divide each term in by and simplify.
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Step 2.5.2.1
Divide each term in by .
Step 2.5.2.2
Simplify the left side.
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Step 2.5.2.2.1
Cancel the common factor of .
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Step 2.5.2.2.1.1
Cancel the common factor.
Step 2.5.2.2.1.2
Divide by .
Step 2.5.2.3
Simplify the right side.
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Step 2.5.2.3.1
Divide by .
Step 3
Evaluate when .
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Step 3.1
Substitute for .
Step 3.2
Substitute for in and solve for .
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Step 3.2.1
Remove parentheses.
Step 3.2.2
Simplify .
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Step 3.2.2.1
Multiply by .
Step 3.2.2.2
Add and .
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