Solve {l}{3{(x-2)}+2{(3x+5)}=3x-5{(2x-1)}}{text{Solvefor}ytext{where}}{y=7}

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

Solve for x, y

$$y=7$$

Solution Steps

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

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

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

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

Combine 3x and 6x to get 9x.

$$9x-6+10=3x-5\left(2x-1\right)$$

Add -6 and 10 to get 4.

$$9x+4=3x-5\left(2x-1\right)$$

Use the distributive property to multiply -5 by 2x-1.

$$9x+4=3x-10x+5$$

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

$$9x+4=-7x+5$$

Add 7x to both sides.

$$9x+4+7x=5$$

Combine 9x and 7x to get 16x.

$$16x+4=5$$

Subtract 4 from both sides.

$$16x=5-4$$

Subtract 4 from 5 to get 1.

$$16x=1$$

Divide both sides by 16.

$$x=\frac{1}{16}$$

The system is now solved.

$$x=\frac{1}{16} y=7$$