Solve {l}{5{(2x-4)}=5}{y=3{(x-2)}-1}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 5 {(2 x - 4)} = 5 }\\ { y = 3 {(x - 2)} - 1 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=\frac{1}{2}=0.5$$

Solution Steps

Consider the first equation. Divide both sides by 5.

$$2x-4=\frac{5}{5}$$

Divide 5 by 5 to get 1.

$$2x-4=1$$

Add 4 to both sides.

$$2x=1+4$$

Add 1 and 4 to get 5.

$$2x=5$$

Divide both sides by 2.

$$x=\frac{5}{2}$$

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

$$y=3\left(\frac{5}{2}-2\right)-1$$

Subtract 2 from \frac{5}{2} to get \frac{1}{2}.

$$y=3\times \frac{1}{2}-1$$

Multiply 3 and \frac{1}{2} to get \frac{3}{2}.

$$y=\frac{3}{2}-1$$

Subtract 1 from \frac{3}{2} to get \frac{1}{2}.

$$y=\frac{1}{2}$$

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

$$z=\frac{1}{2}$$

The system is now solved.

$$x=\frac{5}{2} y=\frac{1}{2} z=\frac{1}{2}$$