Finite Math Examples

Solve the Matrix Equation [[1,x],[2y,-4]]-6[[2,-2],[0,3]]=[[3z,16],[6,-u]]
Step 1
Simplify each term.
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Step 1.1
Multiply by each element of the matrix.
Step 1.2
Simplify each element in the matrix.
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Step 1.2.1
Multiply by .
Step 1.2.2
Multiply by .
Step 1.2.3
Multiply by .
Step 1.2.4
Multiply by .
Step 2
Add the corresponding elements.
Step 3
Simplify each element.
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Step 3.1
Subtract from .
Step 3.2
Add and .
Step 3.3
Subtract from .
Step 4
Write as a linear system of equations.
Step 5
Solve the system of equations.
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Step 5.1
Solve for in .
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Step 5.1.1
Rewrite the equation as .
Step 5.1.2
Divide each term in by and simplify.
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Step 5.1.2.1
Divide each term in by .
Step 5.1.2.2
Simplify the left side.
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Step 5.1.2.2.1
Cancel the common factor of .
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Step 5.1.2.2.1.1
Cancel the common factor.
Step 5.1.2.2.1.2
Divide by .
Step 5.1.2.3
Simplify the right side.
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Step 5.1.2.3.1
Move the negative in front of the fraction.
Step 5.2
Replace all occurrences of with in each equation.
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Step 5.2.1
Move all terms not containing to the right side of the equation.
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Step 5.2.1.1
Subtract from both sides of the equation.
Step 5.2.1.2
Subtract from .
Step 5.2.2
Divide each term in by and simplify.
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Step 5.2.2.1
Divide each term in by .
Step 5.2.2.2
Simplify the left side.
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Step 5.2.2.2.1
Cancel the common factor of .
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Step 5.2.2.2.1.1
Cancel the common factor.
Step 5.2.2.2.1.2
Divide by .
Step 5.2.2.3
Simplify the right side.
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Step 5.2.2.3.1
Divide by .
Step 5.2.3
Rewrite the equation as .
Step 5.2.4
Divide each term in by and simplify.
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Step 5.2.4.1
Divide each term in by .
Step 5.2.4.2
Simplify the left side.
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Step 5.2.4.2.1
Dividing two negative values results in a positive value.
Step 5.2.4.2.2
Divide by .
Step 5.2.4.3
Simplify the right side.
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Step 5.2.4.3.1
Divide by .
Step 5.3
List all of the solutions.