Finite Math Examples

Solve by Substitution y=2x+2 , y=(-1/3)x+14/3
,
Step 1
Eliminate the equal sides of each equation and combine.
Step 2
Solve for .
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Step 2.1
Move all terms containing to the left side of the equation.
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Step 2.1.1
Add to both sides of the equation.
Step 2.1.2
To write as a fraction with a common denominator, multiply by .
Step 2.1.3
Combine and .
Step 2.1.4
Combine the numerators over the common denominator.
Step 2.1.5
Simplify each term.
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Step 2.1.5.1
Simplify the numerator.
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Step 2.1.5.1.1
Factor out of .
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Step 2.1.5.1.1.1
Factor out of .
Step 2.1.5.1.1.2
Raise to the power of .
Step 2.1.5.1.1.3
Factor out of .
Step 2.1.5.1.1.4
Factor out of .
Step 2.1.5.1.2
Multiply by .
Step 2.1.5.1.3
Add and .
Step 2.1.5.2
Move to the left of .
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
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 the numerator.
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Step 2.2.5.1
Multiply by .
Step 2.2.5.2
Subtract from .
Step 2.3
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
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 3
Evaluate when .
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Step 3.1
Substitute for .
Step 3.2
Simplify .
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Step 3.2.1
Combine the numerators over the common denominator.
Step 3.2.2
To write as a fraction with a common denominator, multiply by .
Step 3.2.3
Combine and .
Step 3.2.4
Combine the numerators over the common denominator.
Step 3.2.5
Simplify the numerator.
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Step 3.2.5.1
Multiply by .
Step 3.2.5.2
Add and .
Step 3.2.6
Multiply the numerator by the reciprocal of the denominator.
Step 3.2.7
Cancel the common factor of .
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Step 3.2.7.1
Factor out of .
Step 3.2.7.2
Cancel the common factor.
Step 3.2.7.3
Rewrite the expression.
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