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

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

Solve for x, y

$$x=-\frac{2}{3}\approx -0.666666667$$

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

Solution Steps

Consider the first equation. Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$3x=2\left(-1\right)$$

Multiply 2 and -1 to get -2.

$$3x=-2$$

Divide both sides by 3.

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

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

$$-\frac{2}{3}+\frac{1}{4}=y+\frac{1}{4}$$

Add -\frac{2}{3} and \frac{1}{4} to get -\frac{5}{12}.

$$-\frac{5}{12}=y+\frac{1}{4}$$

Swap sides so that all variable terms are on the left hand side.

$$y+\frac{1}{4}=-\frac{5}{12}$$

Subtract \frac{1}{4} from both sides.

$$y=-\frac{5}{12}-\frac{1}{4}$$

Subtract \frac{1}{4} from -\frac{5}{12} to get -\frac{2}{3}.

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

The system is now solved.

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