Michael P. answered • 10/08/19
MS Mechanical Engineer with Algebra 1 Teaching Experience
The idea is essentially to get one of the equations to the point that the coefficient in front of either the X or the Y term is opposite the coefficient in front of the X or the Y term in the other equation. That usually happens with multiplication.
So, let's talk through it.
Let's call the first Equation A, and the second Equation B.
Because B's coefficient in front of the X term is -1, that's going to be easy to multiple to get to the coefficient in front of the X term in A (3). We multiply by 3. That makes B:
-3x + 6y = 24
Now, we add A and the new B:
3x + 5y = -2
+
-3x + 6y = 24
=
0x + 11y = 22
That's the same as:
11y = 22
We can divide both sides of that equation by 11:
y = 2
Great! Now that we know what Y equals, we can plug its value back into one of the original equations. Let's do so for the original B, because that has small numbers, so the math will be a bit easier:
-x + 2y = 8
-x + 2(2) = 8
-x + 4 = 8
Subtracting 4 from both sides:
-x = 4
Multiplying both sides by -1:
x = -4
That's it! We now know:
y = 2
and
x = -4
