Solve {l}{x-1/4divy+2/3=0}{x+3/5-y-2/4=2}

$$\left.\begin{array} { l } { \frac { x - 1 } { 4 } \div \frac { y + 2 } { 3 } = 0 } \\ { \frac { x + 3 } { 5 } - \frac { y - 2 } { 4 } = 2 } \end{array} \right\}$$

Solve for x, y

$$x=1$$

$$y = -\frac{14}{5} = -2\frac{4}{5} = -2.8$$

Short Solution Steps

Consider the first equation. Divide \frac{x-1}{4} by \frac{y+2}{3} by multiplying \frac{x-1}{4} by the reciprocal of \frac{y+2}{3}.

$$\frac{\left(x-1\right)\times 3}{4\left(y+2\right)}=0$$

Use the distributive property to multiply x-1 by 3.

$$\frac{3x-3}{4\left(y+2\right)}=0$$

Use the distributive property to multiply 4 by y+2.

$$\frac{3x-3}{4y+8}=0$$

Variable y cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by 4\left(y+2\right).

$$3x-3=0$$

Add 3 to both sides. Anything plus zero gives itself.

$$3x=3$$

Divide both sides by 3.

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

Divide 3 by 3 to get 1.

$$x=1$$

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

$$\frac{1+3}{5}-\frac{y-2}{4}=2$$

Multiply both sides of the equation by 20, the least common multiple of 5,4.

$$4\left(1+3\right)-5\left(y-2\right)=40$$

Add 1 and 3 to get 4.

$$4\times 4-5\left(y-2\right)=40$$

Multiply 4 and 4 to get 16.

$$16-5\left(y-2\right)=40$$

Use the distributive property to multiply -5 by y-2.

$$16-5y+10=40$$

Add 16 and 10 to get 26.

$$26-5y=40$$

Subtract 26 from both sides.

$$-5y=40-26$$

Subtract 26 from 40 to get 14.

$$-5y=14$$

Divide both sides by -5.

$$y=-\frac{14}{5}$$

The system is now solved.

$$x=1 y=-\frac{14}{5}$$