Solve {l}{x+3/5-x+3/10-2x-5/3+2=0}{y=5{(2x-3)}-6{(1+2x)}}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{x + 3}{5} - \frac{x + 3}{10} - \frac{2 x - 5}{3} + 2 = 0 }\\ { y = 5 {(2 x - 3)} - 6 {(1 + 2 x)} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=-35$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 30, the least common multiple of 5,10,3.

$$6\left(x+3\right)-3\left(x+3\right)-10\left(2x-5\right)+60=0$$

Use the distributive property to multiply 6 by x+3.

$$6x+18-3\left(x+3\right)-10\left(2x-5\right)+60=0$$

Use the distributive property to multiply -3 by x+3.

$$6x+18-3x-9-10\left(2x-5\right)+60=0$$

Combine 6x and -3x to get 3x.

$$3x+18-9-10\left(2x-5\right)+60=0$$

Subtract 9 from 18 to get 9.

$$3x+9-10\left(2x-5\right)+60=0$$

Use the distributive property to multiply -10 by 2x-5.

$$3x+9-20x+50+60=0$$

Combine 3x and -20x to get -17x.

$$-17x+9+50+60=0$$

Add 9 and 50 to get 59.

$$-17x+59+60=0$$

Add 59 and 60 to get 119.

$$-17x+119=0$$

Subtract 119 from both sides. Anything subtracted from zero gives its negation.

$$-17x=-119$$

Divide both sides by -17.

$$x=\frac{-119}{-17}$$

Divide -119 by -17 to get 7.

$$x=7$$

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

$$y=5\left(2\times 7-3\right)-6\left(1+2\times 7\right)$$

Multiply 2 and 7 to get 14.

$$y=5\left(14-3\right)-6\left(1+2\times 7\right)$$

Subtract 3 from 14 to get 11.

$$y=5\times 11-6\left(1+2\times 7\right)$$

Multiply 5 and 11 to get 55.

$$y=55-6\left(1+2\times 7\right)$$

Multiply 2 and 7 to get 14.

$$y=55-6\left(1+14\right)$$

Add 1 and 14 to get 15.

$$y=55-6\times 15$$

Multiply -6 and 15 to get -90.

$$y=55-90$$

Subtract 90 from 55 to get -35.

$$y=-35$$

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

$$z=-35$$

The system is now solved.

$$x=7 y=-35 z=-35$$