Solve {l}{2(5x-3y)-2y=8-2x}{-3x+5(x-2y)=4-10y}

$$\left\{ \begin{array} { l } { 2 ( 5 x - 3 y ) - 2 y = 8 - 2 x } \\ { - 3 x + 5 ( x - 2 y ) = 4 - 10 y } \end{array} \right.$$

Solve for x, y

$$x=2$$

$$y=2$$

Solution Steps

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

$$10x-6y-2y=8-2x$$

Combine -6y and -2y to get -8y.

$$10x-8y=8-2x$$

Add 2x to both sides.

$$10x-8y+2x=8$$

Combine 10x and 2x to get 12x.

$$12x-8y=8$$

Consider the second equation. Use the distributive property to multiply 5 by x-2y.

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

Combine -3x and 5x to get 2x.

$$2x-10y=4-10y$$

Add 10y to both sides.

$$2x-10y+10y=4$$

Combine -10y and 10y to get 0.

$$2x=4$$

Divide both sides by 2.

$$x=\frac{4}{2}$$

Divide 4 by 2 to get 2.

$$x=2$$

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

$$12\times 2-8y=8$$

Multiply 12 and 2 to get 24.

$$24-8y=8$$

Subtract 24 from both sides.

$$-8y=8-24$$

Subtract 24 from 8 to get -16.

$$-8y=-16$$

Divide both sides by -8.

$$y=\frac{-16}{-8}$$

Divide -16 by -8 to get 2.

$$y=2$$

The system is now solved.

$$x=2 y=2$$