SOLUTION: Hi! I am having problem with solving a system by the addition method. This is one of my problems: 2x + 3y = 1 5x + 3y = 16 2x + 3y =1 -5x - 3y = -16 -3x

SOLUTION: Hi! I am having problem with solving a system by the addition method. This is one of my problems: 2x + 3y = 1 5x + 3y = 16 2x + 3y =1 -5x - 3y = -16 -3x - 2y = -15

Question 17258: Hi! I am having problem with solving a system by the addition method.
This is one of my problems:
2x + 3y = 1
5x + 3y = 16
2x + 3y =1
-5x - 3y = -16
-3x - 2y = -15
-3x = 2y - 15, I'm not sure where to go from here as far as working the problem out. Your help is greatly appreciated. Thank you!!
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
You have 2 equations. Each represents a straight line on the x-y plane.
The solution will be the intersection of the two straight lines.

2x + 3y = 1
5x + 3y = 16
Multiply both sides of the second equation by (-1).
(-1)(5x + 3y) = (-1)(16)
so -5 - 3y = -16
Add this result to the first equation.
2x + 3y = 1
-5x - 3y = -16
-3x = -15 (notice +3y -3y = 0)
Now divide both sides by -3
x = 5
plug this result into first equation.
2(5) + 3y = 1
10 + 3y = 1
subtract 10 from both sides.
3y = -9
divide both sides by 3.
y = -3
If you plug these solutions, x=5 and y= -3 into the original equations,
they should solve both.
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