Question 61342: I need an in depth step by step explaination on how to solve these problems by elimination. 7p+5q=2/8p-9q=17 and 2x+y=13/4x+2y=23
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The goal is to mult one or both equations with values that, when the equations are added or subtracted, one of the unknowns, is eliminated.
:
7p + 5q = 2
8p - 9q =17
:
In this problem, we will choose to eliminate q. We can do this if we mult the 1st equation by 9 and the 2nd equation by 5, we then have:
:
63p + 45q = 18
40p - 45q = 85
---------------- add
103p + 0 = 103
It becomes easy to solve for p
103p = 103
Divide both sides by 103 to get 1p
p = 103/103
p = 1
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Once we know one unknown, in this case it's p=1, we can substitute for p in either equation and find q, we will use the 1st equation:
7(1) + 5q = 2
7 + 5q = 2
Subtract 7 from both sides:
5q = 2 - 7
5q = -5
Divide equation by 5
q = -5/5
q = -1
:
The solutions: p = +1, q = -1
:
Check the solutions in the 2nd equation, substitute for p & q.
8(+1) - 9(-1) = 18
9 - (-9) = 18
Remember a minus a minus is a +
9 + 9 = 18 proves our solutions
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:
:
This system of equations has no solution, inconsistant is what it's called
We can see this if we try to eliminate y by mult the 1st equation by 2 and subtracting:
2x + y = 13
4x +2y = 23
:
4x + 2y = 26
4x + 2y = 23
-------------- subtract
0x + 0y = 3, we eliminated both variables
0 = 3, means there is no values for x and y that will satisfy both equations
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How about this? Can you do this now?
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