Question 37417: The Graphs of ax+by=13 and ax-by=-3 instersect at (1,4). Find a and b.
Found 2 solutions by fractalier, ilana:
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! Since you know both lines go thru (1, 4), you can plug x = 1 and y = 4 in both and get
a + 4b = 13 and
a - 4b = -3
Now add equations and get
2a = 10 and
a = 5
You can also subtract equations and get
8b = 16
b = 2
Answer by ilana(307)  (Show Source):
You can put this solution on YOUR website! Both of these equations are true when x=1 and y=4. So a+4b=13 and a-4b=-3.
By the second equation, a=4b-3, so we can use that in the first and get (4b-3)+4b=13
8b-3=13
8b=16
b=2
a+4b=13, so a+4(2)=13, so a+8=13, so a=5.
So a=5, b=2.
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