Solve {l}{pi/2+y/3=9}{x-y=12}

$$\left. \begin{array} { l } { \frac { \pi } { 2 } + \frac { y } { 3 } = 9 } \\ { x - y = 12 } \end{array} \right.$$

Solve for y, x

$$x=-\frac{3\pi }{2}+39\approx 34.28761102$$

$$y=-\frac{3\pi }{2}+27\approx 22.28761102$$

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.

$$\frac{1}{3}y+\frac{\pi }{2}=9,-y+x=12$$

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.

$$\frac{1}{3}y+\frac{\pi }{2}=9$$

Subtract \frac{\pi }{2} from both sides of the equation.

$$\frac{1}{3}y=-\frac{\pi }{2}+9$$

Multiply both sides by 3.

$$y=-\frac{3\pi }{2}+27$$

Substitute 27-\frac{3\pi }{2} for y in the other equation, -y+x=12.

$$-\left(-\frac{3\pi }{2}+27\right)+x=12$$

Subtract -27+\frac{3\pi }{2} from both sides of the equation.

$$x=-\frac{3\pi }{2}+39$$

The system is now solved.

$$y=-\frac{3\pi }{2}+27,x=-\frac{3\pi }{2}+39$$