Solve {l}{Y=-4/3x-2}{y=2/3x+6}

$$\left. \begin{array} { l } { Y = - \frac { 4 } { 3 } x - 2 } \\ { y = \frac { 2 } { 3 } x + 6 } \end{array} \right.$$

Solve for x, y

$$x=-\frac{3Y}{4}-\frac{3}{2}$$

$$y=-\frac{Y}{2}+5$$

Steps Using Substitution

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

$$-\frac{4}{3}x-2=Y$$

Add 2 to both sides.

$$-\frac{4}{3}x=Y+2$$

Consider the second equation. Subtract \frac{2}{3}x from both sides.

$$y-\frac{2}{3}x=6$$

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.

$$-\frac{4}{3}x=Y+2,-\frac{2}{3}x+y=6$$

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.

$$-\frac{4}{3}x=Y+2$$

Divide both sides of the equation by -\frac{4}{3}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$x=-\frac{3Y}{4}-\frac{3}{2}$$

Substitute -\frac{3Y}{4}-\frac{3}{2} for x in the other equation, -\frac{2}{3}x+y=6.

$$-\frac{2}{3}\left(-\frac{3Y}{4}-\frac{3}{2}\right)+y=6$$

Multiply -\frac{2}{3} times -\frac{3Y}{4}-\frac{3}{2}.

$$\frac{Y}{2}+1+y=6$$

Subtract 1+\frac{Y}{2} from both sides of the equation.

$$y=-\frac{Y}{2}+5$$

The system is now solved.

$$x=-\frac{3Y}{4}-\frac{3}{2},y=-\frac{Y}{2}+5$$