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

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

Solve for x, y, z

$$z=19$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 2 by 3+5x.

$$-3x+5+6+10x-4\left(2x-1\right)=2\left(2-x\right)+4\left(x+1\right)$$

Add 5 and 6 to get 11.

$$-3x+11+10x-4\left(2x-1\right)=2\left(2-x\right)+4\left(x+1\right)$$

Combine -3x and 10x to get 7x.

$$7x+11-4\left(2x-1\right)=2\left(2-x\right)+4\left(x+1\right)$$

Use the distributive property to multiply -4 by 2x-1.

$$7x+11-8x+4=2\left(2-x\right)+4\left(x+1\right)$$

Combine 7x and -8x to get -x.

$$-x+11+4=2\left(2-x\right)+4\left(x+1\right)$$

Add 11 and 4 to get 15.

$$-x+15=2\left(2-x\right)+4\left(x+1\right)$$

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

$$-x+15=4-2x+4\left(x+1\right)$$

Use the distributive property to multiply 4 by x+1.

$$-x+15=4-2x+4x+4$$

Combine -2x and 4x to get 2x.

$$-x+15=4+2x+4$$

Add 4 and 4 to get 8.

$$-x+15=8+2x$$

Subtract 2x from both sides.

$$-x+15-2x=8$$

Combine -x and -2x to get -3x.

$$-3x+15=8$$

Subtract 15 from both sides.

$$-3x=8-15$$

Subtract 15 from 8 to get -7.

$$-3x=-7$$

Divide both sides by -3.

$$x=\frac{-7}{-3}$$

Fraction \frac{-7}{-3} can be simplified to \frac{7}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{7}{3}$$

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

$$y=5\times \frac{7}{3}+1\times 4\times \frac{7}{3}-2$$

Multiply 5 and \frac{7}{3} to get \frac{35}{3}.

$$y=\frac{35}{3}+1\times 4\times \frac{7}{3}-2$$

Multiply 1 and 4 to get 4.

$$y=\frac{35}{3}+4\times \frac{7}{3}-2$$

Multiply 4 and \frac{7}{3} to get \frac{28}{3}.

$$y=\frac{35}{3}+\frac{28}{3}-2$$

Add \frac{35}{3} and \frac{28}{3} to get 21.

$$y=21-2$$

Subtract 2 from 21 to get 19.

$$y=19$$

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

$$z=19$$

The system is now solved.

$$x=\frac{7}{3} y=19 z=19$$