Solve {l}{y_{1}=2x+5}{y=-3x-4}

$$\left. \begin{array} { l } { y _ { 1 } = 2 x + 5 } \\ { y = - 3 x - 4 } \end{array} \right.$$

Solve for x, y

$$x=\frac{y_{1}-5}{2}$$

$$y=\frac{7-3y_{1}}{2}$$

Steps Using Substitution

Consider the first equation. Swap sides so that all variable terms are on the left hand side.

$$2x+5=y_{1}$$

Subtract 5 from both sides.

$$2x=y_{1}-5$$

Consider the second equation. Add 3x to both sides.

$$y+3x=-4$$

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.

$$2x=y_{1}-5,3x+y=-4$$

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

$$2x=y_{1}-5$$

Divide both sides by 2.

$$x=\frac{y_{1}-5}{2}$$

Substitute \frac{y_{1}-5}{2} for x in the other equation, 3x+y=-4.

$$3\times \frac{y_{1}-5}{2}+y=-4$$

Multiply 3 times \frac{y_{1}-5}{2}.

$$\frac{3y_{1}-15}{2}+y=-4$$

Subtract \frac{-15+3y_{1}}{2} from both sides of the equation.

$$y=\frac{7-3y_{1}}{2}$$

The system is now solved.

$$x=\frac{y_{1}-5}{2},y=\frac{7-3y_{1}}{2}$$