Solve {l}{x_{5}+3y=6}{5x+2y=13}

$$\left\{ \begin{array} { l } { x _ { 5 } + 3 y = 6 } \\ { 5 x + 2 y = 13 } \end{array} \right.$$

Solve for x, y

$$x=\frac{2x_{5}}{15}+\frac{9}{5}$$

$$y=-\frac{x_{5}}{3}+2$$

Steps Using Substitution

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.

$$3y+x_{5}=6,2y+5x=13$$

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.

$$3y+x_{5}=6$$

Subtract x_{5} from both sides of the equation.

$$3y=6-x_{5}$$

Divide both sides by 3.

$$y=-\frac{x_{5}}{3}+2$$

Substitute 2-\frac{x_{5}}{3} for y in the other equation, 2y+5x=13.

$$2\left(-\frac{x_{5}}{3}+2\right)+5x=13$$

Multiply 2 times 2-\frac{x_{5}}{3}.

$$-\frac{2x_{5}}{3}+4+5x=13$$

Subtract 4-\frac{2x_{5}}{3} from both sides of the equation.

$$5x=\frac{2x_{5}}{3}+9$$

Divide both sides by 5.

$$x=\frac{2x_{5}}{15}+\frac{9}{5}$$

The system is now solved.

$$y=-\frac{x_{5}}{3}+2,x=\frac{2x_{5}}{15}+\frac{9}{5}$$