Solve {l}{34x-{(8x+6)}-2*3=2*6x-5}{y=5}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 34 x - {(8 x + 6)} - 2 \cdot 3 = 2 \cdot 6 x - 5 }\\ { y = 5 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=5$$

Solution Steps

Consider the first equation. To find the opposite of 8x+6, find the opposite of each term.

$$34x-8x-6-2\times 3=2\times 6x-5$$

Combine 34x and -8x to get 26x.

$$26x-6-2\times 3=2\times 6x-5$$

Multiply 2 and 3 to get 6.

$$26x-6-6=2\times 6x-5$$

Subtract 6 from -6 to get -12.

$$26x-12=2\times 6x-5$$

Multiply 2 and 6 to get 12.

$$26x-12=12x-5$$

Subtract 12x from both sides.

$$26x-12-12x=-5$$

Combine 26x and -12x to get 14x.

$$14x-12=-5$$

Add 12 to both sides.

$$14x=-5+12$$

Add -5 and 12 to get 7.

$$14x=7$$

Divide both sides by 14.

$$x=\frac{7}{14}$$

Reduce the fraction \frac{7}{14} to lowest terms by extracting and canceling out 7.

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

The system is now solved.

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