Solve {l}{x/2=x/3}{x+1/4=y+1/7}

$$\left\{ \begin{array} { l } { \frac { x } { 2 } = \frac { x } { 3 } } \\ { x + \frac { 1 } { 4 } = y + \frac { 1 } { 7 } } \end{array} \right.$$

Solve for x, y

$$x=0$$

$$y=\frac{3}{28}\approx 0.107142857$$

Solution Steps

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

$$3x=2x$$

Subtract 2x from both sides.

$$3x-2x=0$$

Combine 3x and -2x to get x.

$$x=0$$

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

$$0+\frac{1}{4}=y+\frac{1}{7}$$

Add 0 and \frac{1}{4} to get \frac{1}{4}.

$$\frac{1}{4}=y+\frac{1}{7}$$

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

$$y+\frac{1}{7}=\frac{1}{4}$$

Subtract \frac{1}{7} from both sides.

$$y=\frac{1}{4}-\frac{1}{7}$$

Subtract \frac{1}{7} from \frac{1}{4} to get \frac{3}{28}.

$$y=\frac{3}{28}$$

The system is now solved.

$$x=0 y=\frac{3}{28}$$