Solve {l}{4-1*5*{(8x-16)}=40-{(3x-1*4)}}{y=44}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 4 - 1 \cdot 5 \cdot {(8 x - 16)} = 40 - {(3 x - 1 \cdot 4)} }\\ { y = 44 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=44$$

Solution Steps

Consider the first equation. Multiply 1 and 5 to get 5.

$$4-5\left(8x-16\right)=40-\left(3x-1\times 4\right)$$

Use the distributive property to multiply -5 by 8x-16.

$$4-40x+80=40-\left(3x-1\times 4\right)$$

Add 4 and 80 to get 84.

$$84-40x=40-\left(3x-1\times 4\right)$$

Multiply 1 and 4 to get 4.

$$84-40x=40-\left(3x-4\right)$$

To find the opposite of 3x-4, find the opposite of each term.

$$84-40x=40-3x+4$$

Add 40 and 4 to get 44.

$$84-40x=44-3x$$

Add 3x to both sides.

$$84-40x+3x=44$$

Combine -40x and 3x to get -37x.

$$84-37x=44$$

Subtract 84 from both sides.

$$-37x=44-84$$

Subtract 84 from 44 to get -40.

$$-37x=-40$$

Divide both sides by -37.

$$x=\frac{-40}{-37}$$

Fraction \frac{-40}{-37} can be simplified to \frac{40}{37} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{40}{37}$$

The system is now solved.

$$x=\frac{40}{37} y=44 z=44$$