Solve Matrix

$$\left( \begin{array} { l l } { 1 } & { 2 } \\ { 0 } & { 3 } \end{array} \right) \left( \begin{array} { l } { x } \\ { y } \end{array} \right) = \left( \begin{array} { l } { 1 } \\ { 2 } \end{array} \right)$$

Solve for x, y

$$x=-\frac{1}{3}\approx -0.333333333$$

$$y=\frac{2}{3}\approx 0.666666667$$

Solution Steps

Consider the second equation. Divide both sides by 3.

$$y=\frac{2}{3}$$

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

$$x+2\times \frac{2}{3}=1$$

Multiply 2 and \frac{2}{3} to get \frac{4}{3}.

$$x+\frac{4}{3}=1$$

Subtract \frac{4}{3} from both sides.

$$x=1-\frac{4}{3}$$

Subtract \frac{4}{3} from 1 to get -\frac{1}{3}.

$$x=-\frac{1}{3}$$

The system is now solved.

$$x=-\frac{1}{3} y=\frac{2}{3}$$