Solve {l}{2(x+1)=x}{5(y+2)=3y+12}

$$\left. \begin{array} { l } { 2 ( x + 1 ) = x } \\ { 5 ( y + 2 ) = 3 y + 12 } \end{array} \right.$$

Solve for x, y

$$x=-2$$

$$y=1$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 2 by x+1.

$$2x+2=x$$

Subtract x from both sides.

$$2x+2-x=0$$

Combine 2x and -x to get x.

$$x+2=0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$x=-2$$

Consider the second equation. Use the distributive property to multiply 5 by y+2.

$$5y+10=3y+12$$

Subtract 3y from both sides.

$$5y+10-3y=12$$

Combine 5y and -3y to get 2y.

$$2y+10=12$$

Subtract 10 from both sides.

$$2y=12-10$$

Subtract 10 from 12 to get 2.

$$2y=2$$

Divide both sides by 2.

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

Divide 2 by 2 to get 1.

$$y=1$$

The system is now solved.

$$x=-2 y=1$$