Solve {l}{1/3x-3/8x=1}{-1/4x-1/8y=frac{3}{2}}

$$\left. \begin{array} { l } { \frac { 1 } { 3 } x - \frac { 3 } { 8 } x = 1 } \\ { - \frac { 1 } { 4 } x - \frac { 1 } { 8 } y = \frac { 3 } { 2 } } \end{array} \right.$$

Solve for x, y

$$x=-24$$

$$y=36$$

Solution Steps

Consider the first equation. Combine \frac{1}{3}x and -\frac{3}{8}x to get -\frac{1}{24}x.

$$-\frac{1}{24}x=1$$

Multiply both sides by -24, the reciprocal of -\frac{1}{24}.

$$x=1\left(-24\right)$$

Multiply 1 and -24 to get -24.

$$x=-24$$

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

$$-\frac{1}{4}\left(-24\right)-\frac{1}{8}y=\frac{3}{2}$$

Multiply -\frac{1}{4} and -24 to get 6.

$$6-\frac{1}{8}y=\frac{3}{2}$$

Subtract 6 from both sides.

$$-\frac{1}{8}y=\frac{3}{2}-6$$

Subtract 6 from \frac{3}{2} to get -\frac{9}{2}.

$$-\frac{1}{8}y=-\frac{9}{2}$$

Multiply both sides by -8, the reciprocal of -\frac{1}{8}.

$$y=-\frac{9}{2}\left(-8\right)$$

Multiply -\frac{9}{2} and -8 to get 36.

$$y=36$$

The system is now solved.

$$x=-24 y=36$$