Solve {l}{x+3x-9/5=4-5x-12/3}{y=3+3x}{z=5x-2}{a=y}{b=z}{text{Solvefor}c,dtext{where}}{c=a}{d=b}

$$\left. \begin{array} { l } { x + \frac{3 x - 9}{5} = 4 - \frac{5 x - 12}{3} }\\ { y = 3 + 3 x }\\ { z = 5 x - 2 }\\ { a = y }\\ { b = z }\\ { \text{Solve for } c,d \text{ where} } \\ { c = a }\\ { d = b } \end{array} \right.$$

Solve for x, y, z, a, b, c, d

$$c=12$$

$$d=13$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 15, the least common multiple of 5,3.

$$15x+3\left(3x-9\right)=60-5\left(5x-12\right)$$

Use the distributive property to multiply 3 by 3x-9.

$$15x+9x-27=60-5\left(5x-12\right)$$

Combine 15x and 9x to get 24x.

$$24x-27=60-5\left(5x-12\right)$$

Use the distributive property to multiply -5 by 5x-12.

$$24x-27=60-25x+60$$

Add 60 and 60 to get 120.

$$24x-27=120-25x$$

Add 25x to both sides.

$$24x-27+25x=120$$

Combine 24x and 25x to get 49x.

$$49x-27=120$$

Add 27 to both sides.

$$49x=120+27$$

Add 120 and 27 to get 147.

$$49x=147$$

Divide both sides by 49.

$$x=\frac{147}{49}$$

Divide 147 by 49 to get 3.

$$x=3$$

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

$$y=3+3\times 3$$

Multiply 3 and 3 to get 9.

$$y=3+9$$

Add 3 and 9 to get 12.

$$y=12$$

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

$$z=5\times 3-2$$

Multiply 5 and 3 to get 15.

$$z=15-2$$

Subtract 2 from 15 to get 13.

$$z=13$$

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

$$a=12$$

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

$$b=13$$

Consider the equation (6). Insert the known values of variables into the equation.

$$c=12$$

Consider the equation (7). Insert the known values of variables into the equation.

$$d=13$$

The system is now solved.

$$x=3 y=12 z=13 a=12 b=13 c=12 d=13$$