Sorry guys,
there we go again!
4y+6x=80
8x+3y=120
3y+4x=60
9x+2y=150
First line things up. Your format should be ax + by = c for both of them.
6x + 4y = 80
8x + 3y = 120
Now pick either x or y, whichever will be easier. Find the least common multiple. So I will choose y since the numbers are lower. The LCM is 12. Now the trick is that one of the equations has to have a negative sign and the other a plus sign for that variable. So let's make that the first equation.
Multiply the first equation by -3 and the second equation by 4:
-18x - 12y = -240
32x + 12y = 480
Now add similar terms:
14x + 0 = 240
Now solve for x:
x = 120/7
Now plug x into one of the equations and solve for y:
6(120/7) + 4y = 80
720/7 + 4y = 560/7
4y = -160/7
y = -40/7
So you have x = 120/7 and y = -40/7.
Second equation:
4x+3y=60
9x+2y=150
Again we'll work with the y variable since it seems easier. The LCM is 6. So we'll choose the top equation to have the negative sign:
-8x - 6y = -120
27x + 6y = 450
Adding:
19x + 0 = 330
x = 330/19
Plugging into one of the equations (either one):
9(330/19) + 2y = 150
2970/19 + 2y = 2850/19
2y = -120/19
y = -60/19
So we have x = 330/19 and y = -60/19.
The problems on the DAT will likely be much simpler and have integer answers, or maybe at worst a fraction over 2, 3, or something low like that. Not 19 haha.
One last note: sometimes you get problems where one equation has a variable with a coefficient of 1. In that case it MIGHT be easier to just solve for that variable and plug it into the other equation. Use your best judgment.
