Linear Algebra Examples

Solve Using a Matrix by Elimination x=7(y-5) , 4y=3x+5
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Step 1
Move variables to the left and constant terms to the right.
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Step 1.1
Subtract from both sides of the equation.
Step 1.2
Simplify each term.
Step 1.3
Subtract from both sides of the equation.
Step 1.4
Subtract from both sides of the equation.
Step 1.5
Reorder and .
Step 2
Write the system as a matrix.
Step 3
Find the reduced row echelon form.
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Step 3.1
Perform the row operation to make the entry at a .
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Step 3.1.1
Perform the row operation to make the entry at a .
Step 3.1.2
Simplify .
Step 3.2
Multiply each element of by to make the entry at a .
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Step 3.2.1
Multiply each element of by to make the entry at a .
Step 3.2.2
Simplify .
Step 3.3
Perform the row operation to make the entry at a .
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Step 3.3.1
Perform the row operation to make the entry at a .
Step 3.3.2
Simplify .
Step 4
Use the result matrix to declare the final solution to the system of equations.
Step 5
The solution is the set of ordered pairs that make the system true.