EXPLANATION
Given the system of equations
Isolate x for -2x -3y = 12
Add 3y to both sides:
-2x -3y +3y = 12 +3y
Simplify:
-2x = 12 + 3y
Divide both sides by -2
-2x/-2 = 12/-2 + 3y/-2
Simplify:
x = -12/2 + 3y/2
Substitute x = - (12+3y)/2
3(-(12+3y)/2)+2y = 7
Simplify:
(-36-5y)/2 = 7
Isolate y for (-36-5y)/2 = 7
Multiply both sides by 2:
2(-36-5y)/2 = 7*2
Simplify:
-36 -5y = 14
Add 36 to both sides:
-36 -5y + 36 = 14 + 36
Simplify:
-5y = 50
Divide both sides by -5:
-5y/-5 = 50/-5
Simplify:
y= - 10
For x = -(12+3y)/2
Substitute y= -10
x = -(12+3(-10))/2
-(12+3(-10))/2
Remove the parentheses:
= - (12-3*10)/2
Simplifying:
12 - 3* 10 = -18
= -(-18)/2
Apply the fraction rule: (-a)/b = -(a/b)
=-(-18/2)
Divide the numbers
= -(-9)
Apply rule -(-a)=a
=9
So, x=9
The solutions to the system of equations are x=9, y =-10