Linear Algebra Examples

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Solve for in the first equation.
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Subtract from both sides of the equation.
Divide each term by and simplify.
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Divide each term in by .
Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Divide by .
Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Divide by .
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Solve for in the second equation.
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Simplify the left side.
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Simplify each term.
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Apply the distributive property.
Multiply by .
Cancel the common factor of .
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Write as a fraction with denominator .
Factor out the greatest common factor .
Cancel the common factor.
Rewrite the expression.
Multiply and .
Subtract from .
Move all terms not containing to the right side of the equation.
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Subtract from both sides of the equation.
Simplify the right side of the equation.
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To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Multiply by .
Add and .
Move the negative in front of the fraction.
Divide each term by and simplify.
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Divide each term in by .
Simplify the left side of the by cancelling the common factors.
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Reduce the expression by cancelling the common factors.
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Factor out of .
Move the negative one from the denominator of .
Simplify the expression.
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Multiply by .
Rewrite as .
Simplify the right side of the equation.
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Multiply by .
Simplify .
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Multiply by .
Multiply by .
Multiply and .
Multiply by .
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Simplify the right side.
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Multiply by .
To write as a fraction with a common denominator, multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Multiply by .
Multiply by .
Add and .
The solution can be shown in both point and equation forms.
Point Form:
Equation Form:
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