SOLUTION: elimination method a + 9b = 3 a + 4b = -2 Please show me the procedures as well as the solution to the problem

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Question 715567: elimination method
a + 9b = 3
a + 4b = -2
Please show me the procedures as well as the solution to the problem
Found 2 solutions by josgarithmetic, DrBeeee:
Answer by josgarithmetic(39799) About Me  (Show Source):
You can put this solution on YOUR website!
Procedure:

Eliminate a to solve for b.
The coefficients for a in both equations are the same. Just subtract one equation from the other equation.

a + 9b = 3
-a + -4b = -(-2)
------------------
0a+5b=5
b=1

Eliminate b to solve for a
You would want to multiply, in this case, both equations to get the same coefficient on the b terms.
a + 9b = 3
a + 4b = -2

Use 4 as a factor for the first one, and use 9 as a factor for the second one.
4(a + 9b = 3)
9(a + 4b = -2)
You obtain
4a+36b=12
9a+36b=-18

Next, subtract one equation from the other. I will subtract the first from the second.
9a-4a+36b-36b=-18-12
5a+0=-30
5a=30
a=6

Summary of result: a=6 and b=1

Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Given
(1) a + 9b = 3
(2) a + 4b = -2
Simply subtract (2) from (1) and get
(3) a - a + 9b - 4b = 3 -(-2) or
(4) 5b = 5 or
(5) b = 1
Put (5) into (1) and get
(6) a + 9*1 = 3 or
(7) a = 3 - 9 or
(8) a = -6
Let's check with (2).
Is (-6 + 4*1 = -2)?
Is (-6 + 4 = -2)?
Is (-2 = -2)? Yes
Answer: (a,b) = (-6,1).