Algebra Examples

Solve by Addition/Elimination
,
Step 1
Multiply each equation by the value that makes the coefficients of opposite.
Step 2
Simplify.
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Step 2.1
Simplify the left side.
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Step 2.1.1
Simplify .
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Step 2.1.1.1
Apply the distributive property.
Step 2.1.1.2
Multiply by .
Step 2.2
Simplify the right side.
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Step 2.2.1
Multiply by .
Step 3
Add the two equations together to eliminate from the system.
Step 4
Divide each term in by and simplify.
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Step 4.1
Divide each term in by .
Step 4.2
Simplify the left side.
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Step 4.2.1
Cancel the common factor of .
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Step 4.2.1.1
Cancel the common factor.
Step 4.2.1.2
Divide by .
Step 4.3
Simplify the right side.
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Step 4.3.1
Cancel the common factor of and .
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Step 4.3.1.1
Factor out of .
Step 4.3.1.2
Cancel the common factors.
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Step 4.3.1.2.1
Factor out of .
Step 4.3.1.2.2
Cancel the common factor.
Step 4.3.1.2.3
Rewrite the expression.
Step 5
Substitute the value found for into one of the original equations, then solve for .
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Step 5.1
Substitute the value found for into one of the original equations to solve for .
Step 5.2
Simplify each term.
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Step 5.2.1
Multiply .
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Step 5.2.1.1
Combine and .
Step 5.2.1.2
Multiply by .
Step 5.2.2
Move the negative in front of the fraction.
Step 5.3
Move all terms not containing to the right side of the equation.
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Step 5.3.1
Add to both sides of the equation.
Step 5.3.2
To write as a fraction with a common denominator, multiply by .
Step 5.3.3
Combine and .
Step 5.3.4
Combine the numerators over the common denominator.
Step 5.3.5
Simplify the numerator.
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Step 5.3.5.1
Multiply by .
Step 5.3.5.2
Add and .
Step 5.3.6
Move the negative in front of the fraction.
Step 5.4
Divide each term in by and simplify.
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Step 5.4.1
Divide each term in by .
Step 5.4.2
Simplify the left side.
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Step 5.4.2.1
Cancel the common factor of .
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Step 5.4.2.1.1
Cancel the common factor.
Step 5.4.2.1.2
Divide by .
Step 5.4.3
Simplify the right side.
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Step 5.4.3.1
Multiply the numerator by the reciprocal of the denominator.
Step 5.4.3.2
Cancel the common factor of .
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Step 5.4.3.2.1
Move the leading negative in into the numerator.
Step 5.4.3.2.2
Factor out of .
Step 5.4.3.2.3
Factor out of .
Step 5.4.3.2.4
Cancel the common factor.
Step 5.4.3.2.5
Rewrite the expression.
Step 5.4.3.3
Multiply by .
Step 5.4.3.4
Multiply by .
Step 5.4.3.5
Dividing two negative values results in a positive value.
Step 6
The solution to the independent system of equations can be represented as a point.
Step 7
The result can be shown in multiple forms.
Point Form:
Equation Form:
Step 8
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