Solve {l}{30-(8)=2y+30}{5x-29=x-(5-4y)}

$$\left\{ \begin{array} { l } { 30 - ( 8 ) = 2 y + 30 } \\ { 5 x - 29 = x - ( 5 - 4 y ) } \end{array} \right.$$

Solve for y, x

$$x=2$$

$$y=-4$$

Solution Steps

Consider the first equation. Subtract 8 from 30 to get 22.

$$22=2y+30$$

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

$$2y+30=22$$

Subtract 30 from both sides.

$$2y=22-30$$

Subtract 30 from 22 to get -8.

$$2y=-8$$

Divide both sides by 2.

$$y=\frac{-8}{2}$$

Divide -8 by 2 to get -4.

$$y=-4$$

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

$$5x-29=x-\left(5-4\left(-4\right)\right)$$

Multiply -4 and -4 to get 16.

$$5x-29=x-\left(5+16\right)$$

Add 5 and 16 to get 21.

$$5x-29=x-21$$

Subtract x from both sides.

$$5x-29-x=-21$$

Combine 5x and -x to get 4x.

$$4x-29=-21$$

Add 29 to both sides.

$$4x=-21+29$$

Add -21 and 29 to get 8.

$$4x=8$$

Divide both sides by 4.

$$x=\frac{8}{4}$$

Divide 8 by 4 to get 2.

$$x=2$$

The system is now solved.

$$y=-4 x=2$$