Solve {l}{x+2(x+2y)=40}{x_{1}+2y=2}

$$\left\{ \begin{array} { l } { x + 2 ( x + 2 y ) = 40 } \\ { x _ { 1 } + 2 y = 2 } \end{array} \right.$$

Solve for x, y

$$x=\frac{2x_{1}}{3}+12$$

$$y=-\frac{x_{1}}{2}+1$$

Steps Using Substitution

Consider the second equation. Subtract x_{1} from both sides.

$$2y=2-x_{1}$$

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

$$x+2x+4y=40$$

Combine x and 2x to get 3x.

$$3x+4y=40$$

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

$$2y=2-x_{1},4y+3x=40$$

Pick one of the two equations which is more simple to solve for y by isolating y on the left hand side of the equal sign.

$$2y=2-x_{1}$$

Divide both sides by 2.

$$y=-\frac{x_{1}}{2}+1$$

Substitute 1-\frac{x_{1}}{2} for y in the other equation, 4y+3x=40.

$$4\left(-\frac{x_{1}}{2}+1\right)+3x=40$$

Multiply 4 times 1-\frac{x_{1}}{2}.

$$4-2x_{1}+3x=40$$

Subtract 4-2x_{1} from both sides of the equation.

$$3x=2x_{1}+36$$

Divide both sides by 3.

$$x=\frac{2x_{1}}{3}+12$$

The system is now solved.

$$y=-\frac{x_{1}}{2}+1,x=\frac{2x_{1}}{3}+12$$