Solve {l}{2(y-x)+4=2y}{y-(x+1)^2=2-(x-1)^2}

$$\left\{ \begin{array} { l } { 2 ( y - x ) + 4 = 2 y } \\ { y - ( x + 1 ) ^ { 2 } = 2 - ( x - 1 ) ^ { 2 } } \end{array} \right.$$

Solve for y, x

$$x=2$$

$$y=10$$

Solution Steps

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

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

Subtract 2y from both sides.

$$2y-2x+4-2y=0$$

Combine 2y and -2y to get 0.

$$-2x+4=0$$

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$-2x=-4$$

Divide both sides by -2.

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

Divide -4 by -2 to get 2.

$$x=2$$

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

$$y-\left(2+1\right)^{2}=2-\left(2-1\right)^{2}$$

Add 2 and 1 to get 3.

$$y-3^{2}=2-\left(2-1\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$y-9=2-\left(2-1\right)^{2}$$

Subtract 1 from 2 to get 1.

$$y-9=2-1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$y-9=2-1$$

Subtract 1 from 2 to get 1.

$$y-9=1$$

Add 9 to both sides.

$$y=1+9$$

Add 1 and 9 to get 10.

$$y=10$$

The system is now solved.

$$y=10 x=2$$