# How do you solve the system -2x+15y=-24, 2x+9y=24?

Nov 30, 2016

$x = 12$ and $y = 0$

#### Explanation:

Step 1) Solve the first equation for $x$:

$- 2 x + 15 y - 15 y = - 24 - 15 y$

$- 2 x = - 24 - 15 y$

$\frac{- 2 x}{-} 2 = \frac{- 24 - 15 y}{-} 2$

$x = 12 + \frac{15}{2} y$

Step 2) Substitute $12 + \frac{15}{2} y$ for $x$ in the second equation and solve for $y$:

2(12 + 15/2y) + 9y = 24

24 + 15y + 9y = 24

$24 + 24 y = 24$

$24 - 24 + 24 y = 24 - 24$

$24 y = 0$

#(24y)/24 = 0/24$$y = 0$Step 3) Substitute $0$for $y$in the solution to the equation in Step 1) and calculate $x$: $x = 12 + \left(\frac{15}{2} \cdot 0\right)$$x = 12 + 0$$x = 12\$