Solve Matrix

$$\left( \begin{array} { l l } { x } & { 3 } \end{array} \right) \left( \begin{array} { l l } { 2 } & { 5 } \\ { x } & { - y } \end{array} \right) = \left( \begin{array} { l l } { 20 } & { y } \end{array} \right)$$

Solve for x, y

$$x=4$$

$$y=5$$

Solution Steps

Consider the first equation. Divide both sides by 5.

$$x=\frac{20}{5}$$

Divide 20 by 5 to get 4.

$$x=4$$

Consider the second equation. Insert the known values of variables into the equation.

$$5\times 4-3y=y$$

Multiply 5 and 4 to get 20.

$$20-3y=y$$

Subtract y from both sides.

$$20-3y-y=0$$

Combine -3y and -y to get -4y.

$$20-4y=0$$

Subtract 20 from both sides. Anything subtracted from zero gives its negation.

$$-4y=-20$$

Divide both sides by -4.

$$y=\frac{-20}{-4}$$

Divide -20 by -4 to get 5.

$$y=5$$

The system is now solved.

$$x=4 y=5$$