Hi,

Is the a shortcut or quicker way to solve this Simultaneous Equations?
thanks

4y+6x=80 8x+3y=120

3y+4x=60 9x+2y=150

can you plz post the problem more clearly.
4y+6x=80 8x+3y=120 is that problem #1?
3y+4x=60 9x+2y=150 is that problem #2?


or is it 4y+6x=80 3y+4x=60
and 8x+3y=120 9x+2y=150
-thanks :)

can you plz post the problem more clearly.
4y+6x=80 8x+3y=120 is that problem #1?
3y+4x=60 9x+2y=150 is that problem #2?


or is it 4y+6x=80 3y+4x=60
and 8x+3y=120 9x+2y=150
-thanks :)

I was about to say the same thing :laugh:

Sorry guys,
there we go again!:laugh:


4y+6x=80
8x+3y=120

3y+4x=60
9x+2y=150

Sorry guys,
there we go again!:laugh:


4y+6x=80
8x+3y=120

3y+4x=60
9x+2y=150

When you have two simultaneous equations, pick one equation, solve for the variable of your choice, and plug it into the second equation. Then solve for the remaining variable.

4y+6x=80
y = (80-6x)/4

8x + 3[(80-6x)/4] = 120

solve for x

plug the numerical value of x into the original equation to solve for y.

Sorry guys,
there we go again!:laugh:


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.