Solve {l}{3(x-10)=2x-10}{3(y-10)=2y-10x/2}

$$\left\{ \begin{array} { l } { 3 ( x - 10 ) = 2 x - 10 } \\ { 3 ( y - 10 ) = 2 y - 10 \frac { x } { 2 } } \end{array} \right.$$

Solve for x, y

$$x=20$$

$$y=-70$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 3 by x-10.

$$3x-30=2x-10$$

Subtract 2x from both sides.

$$3x-30-2x=-10$$

Combine 3x and -2x to get x.

$$x-30=-10$$

Add 30 to both sides.

$$x=-10+30$$

Add -10 and 30 to get 20.

$$x=20$$

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

$$3\left(y-10\right)=2y-10\times \frac{20}{2}$$

Use the distributive property to multiply 3 by y-10.

$$3y-30=2y-10\times \frac{20}{2}$$

Divide 20 by 2 to get 10.

$$3y-30=2y-10\times 10$$

Multiply 10 and 10 to get 100.

$$3y-30=2y-100$$

Subtract 2y from both sides.

$$3y-30-2y=-100$$

Combine 3y and -2y to get y.

$$y-30=-100$$

Add 30 to both sides.

$$y=-100+30$$

Add -100 and 30 to get -70.

$$y=-70$$

The system is now solved.

$$x=20 y=-70$$