Solve the system of equations using the Addition method.
2a + 3b = -1
3a + 5b = -2
The addition method tells you to find common multiples of a coefficient, then add the equations together to eliminate a variable.
If you multiply the first equation by 3 and the second by -2 you have
2a + 3b = -1
3a + 5b = -2
becomes
3 (2a + 3b = -1)
-2(3a + 5b = -2)
which is
6a + 9b = -3
-6a-10b = 4
Now add together to get
-b=1 or b=-1
Now substitute into either equation and solve for a.
Let's substitute the value of b back into one of the original equations. Let's use the first equation:
2a + 3b = -1
Substituting b = -1, we have:
2a + 3(-1) = -1
Simplifying this equation gives us:
2a - 3 = -1
Now let's solve for a:
2a - 3 = -1
2a = 2
a = 1
So the solution to the system of equations is a = 1 and b = -1.