Solve {l}{4{(x-1)}-1*2{(2x-2)}=7{(0*5-x)}+2{(2*25+3x)}}{y=3}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 4 {(x - 1)} - 1 \cdot 2 {(2 x - 2)} = 7 {(0 \cdot 5 - x)} + 2 {(2 \cdot 25 + 3 x)} }\\ { y = 3 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=3$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 4 by x-1.

$$4x-4-1\times 2\left(2x-2\right)=7\left(0\times 5-x\right)+2\left(2\times 25+3x\right)$$

Multiply 1 and 2 to get 2.

$$4x-4-2\left(2x-2\right)=7\left(0\times 5-x\right)+2\left(2\times 25+3x\right)$$

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

$$4x-4-4x+4=7\left(0\times 5-x\right)+2\left(2\times 25+3x\right)$$

Combine 4x and -4x to get 0.

$$-4+4=7\left(0\times 5-x\right)+2\left(2\times 25+3x\right)$$

Add -4 and 4 to get 0.

$$0=7\left(0\times 5-x\right)+2\left(2\times 25+3x\right)$$

Multiply 0 and 5 to get 0.

$$0=7\left(0-x\right)+2\left(2\times 25+3x\right)$$

Anything plus zero gives itself.

$$0=7\left(-1\right)x+2\left(2\times 25+3x\right)$$

Multiply 7 and -1 to get -7.

$$0=-7x+2\left(2\times 25+3x\right)$$

Multiply 2 and 25 to get 50.

$$0=-7x+2\left(50+3x\right)$$

Use the distributive property to multiply 2 by 50+3x.

$$0=-7x+100+6x$$

Combine -7x and 6x to get -x.

$$0=-x+100$$

Swap sides so that all variable terms are on the left hand side.

$$-x+100=0$$

Subtract 100 from both sides. Anything subtracted from zero gives its negation.

$$-x=-100$$

Divide both sides by -1.

$$x=\frac{-100}{-1}$$

Fraction \frac{-100}{-1} can be simplified to 100 by removing the negative sign from both the numerator and the denominator.

$$x=100$$

The system is now solved.

$$x=100 y=3 z=3$$