First off, never call yourself stupid! I can't fix my own car. That doesn't make me stupid. That's why I have a mechanic.
3x + 2y = 4
4x + 3y = 7
This used to confuse me, too. We can take an equation and multiply it by one factor, and it will still produce the same graph.
125(3x + 2y) = 125(4)
375x + 250y = 500
Believe it or not, 375x + 250y = 500 is the same as 3x + 2y = 125.
My point? We need to make one of the variables cancel out. We do that by making them opposites, because opposites add up to 0 and cancel out. Let's do x.
What's the LCM of 3 and 4? 12. If we multiply 3(-4) and 4(3), we now have -12 and 12, which add to 0.
-4(3x + 2y) = -4(4)
3(4x + 3y) = 3(7)
-12x - 8y = -16
12x + 9y = 21
Now, if we add the two equations together, we get...
y = 5
Wow, no more steps to solve for y. Now we can put that into either equation and solve for x.
3x + 2(5) = 4
3x + 10 = 4
3x = -6
x = -2
So, there ya go. Your solution (the point where both lines meet and makes both equations true) is (-2,5).
Let's check.
3(-2) + 2(5) = 4
-6 + 10 = 4
4 = 4
0 = 0
4(-2) + 3(5) = 7
-8 + 15 = 7
7 = 7
0 = 0
Hey, we got it right!
