Solve {l}{3x+12=2x}{y/7+y-4/3=2}

$$\left. \begin{array} { l } { 3 x + 12 = 2 x } \\ { \frac { y } { 7 } + \frac { y - 4 } { 3 } = 2 } \end{array} \right.$$

Solve for x, y

$$x=-12$$

$$y=7$$

Solution Steps

Consider the first equation. Subtract 2x from both sides.

$$3x+12-2x=0$$

Combine 3x and -2x to get x.

$$x+12=0$$

Subtract 12 from both sides. Anything subtracted from zero gives its negation.

$$x=-12$$

Consider the second equation. Multiply both sides of the equation by 21, the least common multiple of 7,3.

$$3y+7\left(y-4\right)=42$$

Use the distributive property to multiply 7 by y-4.

$$3y+7y-28=42$$

Combine 3y and 7y to get 10y.

$$10y-28=42$$

Add 28 to both sides.

$$10y=42+28$$

Add 42 and 28 to get 70.

$$10y=70$$

Divide both sides by 10.

$$y=\frac{70}{10}$$

Divide 70 by 10 to get 7.

$$y=7$$

The system is now solved.

$$x=-12 y=7$$