Solve {l}{x-{(5+3x-{(5x-{(6+x)})})}=-3}{y=9x-{(5x+1)}-52+8x-{(7x-5)}}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { x - {(5 + 3 x - {(5 x - {(6 + x)})})} = -3 }\\ { y = 9 x - {(5 x + 1)} - 52 + 8 x - {(7 x - 5)} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=-28$$

Solution Steps

Consider the first equation. To find the opposite of 6+x, find the opposite of each term.

$$x-\left(5+3x-\left(5x-6-x\right)\right)=-3$$

Combine 5x and -x to get 4x.

$$x-\left(5+3x-\left(4x-6\right)\right)=-3$$

To find the opposite of 4x-6, find the opposite of each term.

$$x-\left(5+3x-4x+6\right)=-3$$

Combine 3x and -4x to get -x.

$$x-\left(5-x+6\right)=-3$$

Add 5 and 6 to get 11.

$$x-\left(11-x\right)=-3$$

To find the opposite of 11-x, find the opposite of each term.

$$x-11+x=-3$$

Combine x and x to get 2x.

$$2x-11=-3$$

Add 11 to both sides.

$$2x=-3+11$$

Add -3 and 11 to get 8.

$$2x=8$$

Divide both sides by 2.

$$x=\frac{8}{2}$$

Divide 8 by 2 to get 4.

$$x=4$$

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

$$y=9\times 4-\left(5\times 4+1\right)-52+8\times 4-\left(7\times 4-5\right)$$

Do the multiplications.

$$y=36-\left(5\times 4+1\right)-52+32-\left(7\times 4-5\right)$$

Multiply 5 and 4 to get 20.

$$y=36-\left(20+1\right)-52+32-\left(7\times 4-5\right)$$

Add 20 and 1 to get 21.

$$y=36-21-52+32-\left(7\times 4-5\right)$$

Subtract 21 from 36 to get 15.

$$y=15-52+32-\left(7\times 4-5\right)$$

Subtract 52 from 15 to get -37.

$$y=-37+32-\left(7\times 4-5\right)$$

Add -37 and 32 to get -5.

$$y=-5-\left(7\times 4-5\right)$$

Multiply 7 and 4 to get 28.

$$y=-5-\left(28-5\right)$$

Subtract 5 from 28 to get 23.

$$y=-5-23$$

Subtract 23 from -5 to get -28.

$$y=-28$$

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

$$z=-28$$

The system is now solved.

$$x=4 y=-28 z=-28$$