Solve {l}{-{(1-5x)}=7-2{(1-x)}}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { -{(1 - 5 x)} = 7 - 2 {(1 - x)} }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=2$$

Solution Steps

Consider the first equation. To find the opposite of 1-5x, find the opposite of each term.

$$-1+5x=7-2\left(1-x\right)$$

Use the distributive property to multiply -2 by 1-x.

$$-1+5x=7-2+2x$$

Subtract 2 from 7 to get 5.

$$-1+5x=5+2x$$

Subtract 2x from both sides.

$$-1+5x-2x=5$$

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

$$-1+3x=5$$

Add 1 to both sides.

$$3x=5+1$$

Add 5 and 1 to get 6.

$$3x=6$$

Divide both sides by 3.

$$x=\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$x=2$$

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

$$y=2$$

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

$$z=2$$

The system is now solved.

$$x=2 y=2 z=2$$