Find the Variables [[1,3],[1,4]][[x],[y]]=[[5],[6]]

$[\begin{array}{c} 1 & 3 \\ 1 & 4 \end{array}] [\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} 5 \\ 6 \end{array}]$

Simplify the left side of the equation.

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

$[\begin{array}{c} 1 \cdot x + 3 \cdot y \\ 1 \cdot x + 4 \cdot y \end{array}] = [\begin{array}{c} 5 \\ 6 \end{array}]$

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

$[\begin{array}{c} x + 3 y \\ x + 4 y \end{array}] = [\begin{array}{c} 5 \\ 6 \end{array}]$

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

$x + 3 y = 5$

$x + 4 y = 6$

Subtract $3 y$ from both sides of the equation.

$x = 5 - 3 y$

$x + 4 y = 6$

Replace all occurrences of $x$ with $5 - 3 y$ in each equation.

Replace all occurrences of $x$ in $x + 4 y = 6$ with $5 - 3 y$ .

$(5 - 3 y) + 4 y = 6$

$x = 5 - 3 y$

Simplify the left side.

Add $- 3 y$ and $4 y$ .

$5 + y = 6$

$x = 5 - 3 y$

$5 + y = 6$

$x = 5 - 3 y$

$5 + y = 6$

$x = 5 - 3 y$

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

Subtract $5$ from both sides of the equation.

$y = 6 - 5$

$x = 5 - 3 y$

Subtract $5$ from $6$ .

$y = 1$

$x = 5 - 3 y$

$y = 1$

$x = 5 - 3 y$

Replace all occurrences of $y$ with $1$ in each equation.

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

$x = 5 - 3 \cdot 1$

$y = 1$

Simplify the right side.

Simplify $5 - 3 \cdot 1$ .

Multiply $- 3$ by $1$ .

$x = 5 - 3$

$y = 1$

Subtract $3$ from $5$ .

$x = 2$

$y = 1$

$x = 2$

$y = 1$

$x = 2$

$y = 1$

$x = 2$

$y = 1$

List all of the solutions.

$x = 2, y = 1$

Find the Variables [[1,3],[1,4]][[x],[y]]=[[5],[6]]

Related Questions

Support LCMGCF.com by disabling your adblocker.