Explanation
Let's solve the 1st equation for the variable y.
-5x+y = -2
y = 5x-2
Then we'll plug this into the 2nd equation to solve for x. We're substituting each copy of y with 5x-2.
-3x+6y = -12
-3x+6(5x-2) = -12
-3x+30x-12 = -12
27x-12 = -12
27x = -12+12
27x = 0
x = 0/27
x = 0
Use this x value to determine the value of y.
y = 5x-2
y = 5*0-2
y = 0 - 2
y = -2
The solution as an ordered pair is (x,y) = (0, -2)
This is where the two lines intersect. You can use a graphing tool like Desmos or GeoGebra to confirm.
