Finite Math Examples

$x - y = 1$ , $- x + y = - 1$

Step 1

Write the system as a matrix.

$[\begin{array}{c} 1 & - 1 & 1 \\ - 1 & 1 & - 1 \end{array}]$

Step 2

Find the reduced row echelon form.

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Step 2.1

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

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Step 2.1.1

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

$[\begin{array}{c} 1 & - 1 & 1 \\ - 1 + 1 \cdot 1 & 1 - 1 & - 1 + 1 \cdot 1 \end{array}]$

Step 2.1.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & - 1 & 1 \\ 0 & 0 & 0 \end{array}]$

Step 3

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

$x - y = 1$

$0 = 0$

Step 4

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

$(1 + y, y)$