Solve {l}{5{(5-7x)}=8-{(4x+6)}}{y=0}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 5 {(5 - 7 x)} = 8 - {(4 x + 6)} }\\ { y = 0 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=0$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 5 by 5-7x.

$$25-35x=8-\left(4x+6\right)$$

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

$$25-35x=8-4x-6$$

Subtract 6 from 8 to get 2.

$$25-35x=2-4x$$

Add 4x to both sides.

$$25-35x+4x=2$$

Combine -35x and 4x to get -31x.

$$25-31x=2$$

Subtract 25 from both sides.

$$-31x=2-25$$

Subtract 25 from 2 to get -23.

$$-31x=-23$$

Divide both sides by -31.

$$x=\frac{-23}{-31}$$

Fraction \frac{-23}{-31} can be simplified to \frac{23}{31} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{23}{31}$$

The system is now solved.

$$x=\frac{23}{31} y=0 z=0$$