How do you solve the system of equations 2x + 5y = 6 and - 2x - 3y = 6?

1 Answer
Sep 6, 2017

x=-12
y=6

Explanation:

Finding x is gonna be a bit long so here it is:

Label 2x+5y = 6 and -2x-3y = 6 as Equation 1 and 2 respectively.

Seeing as the y variables aren't equal, multiply Eq. 1 by 3 to get 15y and multiply Eq.2 by 5 to get -15y:

Eq 1 * 3:
6x + 15y = 18

Eq 2 * 5
-10x - 15y = 30

Label these new equations as Eq 3 and 4, respectively.

Add these two equations together:
Eq. 3 + Eq. 4

6x + 15y = 18
-10x - 15y = 30

=-4x = 48
x = -12

To find y, substitute the value of x into one of the equations:
2(-12)+5y =6
-24 + 5y = 6
5y = 6+24
5y = 30
y=6

Hope this helps!