Question 35125
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.