Finite Math Examples

$x + 5 y = 10$ , $3 x + 15 y = 30$

Step 1

Write the system as a matrix.

$[\begin{array}{c} 1 & 5 & 10 \\ 3 & 15 & 30 \end{array}]$

Step 2

Find the reduced row echelon form.

Tap for more steps...

Step 2.1

Perform the row operation $R_{2} = R_{2} - 3 R_{1}$ to make the entry at $2, 1$ a $0$ .

Tap for more steps...

Step 2.1.1

Perform the row operation $R_{2} = R_{2} - 3 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 5 & 10 \\ 3 - 3 \cdot 1 & 15 - 3 \cdot 5 & 30 - 3 \cdot 10 \end{array}]$

Step 2.1.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & 5 & 10 \\ 0 & 0 & 0 \end{array}]$

Step 3

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

$x + 5 y = 10$

$0 = 0$

Step 4

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

$(10 - 5 y, y)$