Find the Variables [[1,-3],[-5,16]][[x],[y]]=[[-1],[5]]

$[\begin{array}{c} 1 & - 3 \\ - 5 & 16 \end{array}] [\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} - 1 \\ 5 \end{array}]$

Simplify the left side of the equation.

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

$[\begin{array}{c} 1 \cdot x - 3 \cdot y \\ - 5 \cdot x + 16 \cdot y \end{array}] = [\begin{array}{c} - 1 \\ 5 \end{array}]$

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

$[\begin{array}{c} x - 3 y \\ - 5 x + 16 y \end{array}] = [\begin{array}{c} - 1 \\ 5 \end{array}]$

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

$x - 3 y = - 1$

$- 5 x + 16 y = 5$

Add $3 y$ to both sides of the equation.

$x = - 1 + 3 y$

$- 5 x + 16 y = 5$

Replace all occurrences of $x$ with $- 1 + 3 y$ in each equation.

Replace all occurrences of $x$ in $- 5 x + 16 y = 5$ with $- 1 + 3 y$ .

$- 5 (- 1 + 3 y) + 16 y = 5$

$x = - 1 + 3 y$

Simplify the left side.

Simplify $- 5 (- 1 + 3 y) + 16 y$ .

Simplify each term.

Apply the distributive property.

$- 5 \cdot - 1 - 5 (3 y) + 16 y = 5$

$x = - 1 + 3 y$

Multiply $- 5$ by $- 1$ .

$5 - 5 (3 y) + 16 y = 5$

$x = - 1 + 3 y$

Multiply $3$ by $- 5$ .

$5 - 15 y + 16 y = 5$

$x = - 1 + 3 y$

$5 - 15 y + 16 y = 5$

$x = - 1 + 3 y$

Add $- 15 y$ and $16 y$ .

$5 + y = 5$

$x = - 1 + 3 y$

$5 + y = 5$

$x = - 1 + 3 y$

$5 + y = 5$

$x = - 1 + 3 y$

$5 + y = 5$

$x = - 1 + 3 y$

Move all terms not containing $y$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$y = 5 - 5$

$x = - 1 + 3 y$

Subtract $5$ from $5$ .

$y = 0$

$x = - 1 + 3 y$

$y = 0$

$x = - 1 + 3 y$

Replace all occurrences of $y$ with $0$ in each equation.

Replace all occurrences of $y$ in $x = - 1 + 3 y$ with $0$ .

$x = - 1 + 3 (0)$

$y = 0$

Simplify the right side.

Simplify $- 1 + 3 (0)$ .

Multiply $3$ by $0$ .

$x = - 1 + 0$

$y = 0$

Add $- 1$ and $0$ .

$x = - 1$

$y = 0$

$x = - 1$

$y = 0$

$x = - 1$

$y = 0$

$x = - 1$

$y = 0$

List all of the solutions.

$x = - 1, y = 0$

Find the Variables [[1,-3],[-5,16]][[x],[y]]=[[-1],[5]]

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