Algebra Examples

$[\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} 0 & 1 \\ 1 & 2 \end{array}] [\begin{array}{c} 7 \\ - 3 \end{array}]$

Step 1

Simplify the right side of the equation.

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Multiply each row in the first matrix by each column in the second matrix.

$[\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} 0 \cdot 7 + 1 \cdot - 3 \\ 1 \cdot 7 + 2 \cdot - 3 \end{array}]$

Simplify each element of the matrix by multiplying out all the expressions.

$[\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} - 3 \\ 1 \end{array}]$

Step 2

The matrix equation can be written as a set of equations.

$x = - 3$

$y = 1$

Step 3

The system is already solved.

$x = - 3, y = 1$