Finite Math Examples

$x + 5 y - 5 z = - 23$ , $y - 2 z = - 3$

Step 1

Write the system as a matrix.

$[\begin{array}{c} 1 & 5 & - 5 & - 23 \\ 0 & 1 & - 2 & - 3 \end{array}]$

Step 2

Find the reduced row echelon form.

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Step 2.1

Perform the row operation $R_{1} = R_{1} - 5 R_{2}$ to make the entry at $1, 2$ a $0$ .

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Step 2.1.1

Perform the row operation $R_{1} = R_{1} - 5 R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - 5 \cdot 0 & 5 - 5 \cdot 1 & - 5 - 5 \cdot - 2 & - 23 - 5 \cdot - 3 \\ 0 & 1 & - 2 & - 3 \end{array}]$

Step 2.1.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 5 & - 8 \\ 0 & 1 & - 2 & - 3 \end{array}]$

Step 3

Use the result matrix to declare the final solution to the system of equations.

$x + 5 z = - 8$

$y - 2 z = - 3$

Step 4

The solution is the set of ordered pairs that make the system true.

$(- 8 - 5 z, - 3 + 2 z, z)$