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Question 35125: I need to find the intercept point of y=3x+8 and 4x+2y=6. If you can find the answer, would you explain it to me? I also have a few more to do and I need to understand how to do it.
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! each is just a straight line, so if they cross, will be equal at that one point...the solution.
As to how to do it: at that one point, the x,y values in both equation are the same eg at x=2, then y will be whatever, but both equations will give the same answer...the point is the same on both lines.
OK, i have laboured the point enough. Method:
y=3x+8 and 4x+2y=6
--> 2y=6x+16 is the first equation scalled up by factor of 2. Why did i do that? Well, now both equations have a "2y" term, so i can put one version into the other equation and just have an equation in "x", so i can solve that:
sub 6x+16 in place of 2y in 4x+2y=6
--> 4x+(6x+16)=6
4x+6x+16=6
10x+16=6
10x=-10
x=-10/10
--> x=-1
and so from y=3x+8 (or the other one, it doesn't matter: i just picked the simplest one to work with) and knowing that x=-1, we get
y=3(-1)+8
y=-3+8
y=5
So the solution is x=-1, y=5
CHECK other equation:
4x+2y=6
4(-1)+2(5)
-4+10
6 --> which is what the equation does equal, so we KNOW we have the correct answer.
Move on to next question, happy that you KNOW it is correct :-)
jon.
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