Please help...I just don't get it

[completelyLost]

Brief bg. Im in my 40's attempting to pass the gmat exam. I have never and I mean never understood algebra. I can code software and completely rebuild motors, but I cannot understand algebra. Please help!

I am taking a self learning algebra course online and have to solve sets of linear equations. The following are the equations.

4x-9y=0
3x+2y=35

I try to add them:
7x-7y=35

Then I'm stuck. I just don't get it. Am I even on the right track by beginning this way? How do I remove the x or the y? Do I add 7y to both sides? Do I subtract 7x to both sides? How do I isolate x or y?

 

[lex]

(1) 4x-9y=0
(2) 3x+2y=35

Let's say, multiply the first equation by 3 and the second one by 4:

12x-27y=0
12x+8y=140

Now you can subtract these equations (2nd equation - 1st equation), to find y and then hopefully using this value of y, go back to equation (2) say, and find x.

(Alternatively you could have multiplied the first equation by 2 and the second one by 9:

8x-18y=0
27x+18y=315

Then you could add these equations to find x, and then find y, using this value of x in equation (2) say).

 

[lev888]

Brief bg. Im in my 40's attempting to pass the gmat exam. I have never and I mean never understood algebra. I can code software and completely rebuild motors, but I cannot understand algebra. Please help!

I am taking a self learning algebra course online and have to solve sets of linear equations. The following are the equations.

4x-9y=0
3x+2y=35

I try to add them:
7x-7y=35

Then I'm stuck. I just don't get it. Am I even on the right track by beginning this way? How do I remove the x or the y? Do I add 7y to both sides? Do I subtract 7x to both sides? How do I isolate x or y?

Please see the first reply for one approach. Another would be to express one variable through the other using one equation, then substitute it into the other equation and solve it, then substitute the found value into the expression.

 

[Deleted member 4993]

Brief bg. Im in my 40's attempting to pass the gmat exam. I have never and I mean never understood algebra. I can code software and completely rebuild motors, but I cannot understand algebra. Please help!

I am taking a self learning algebra course online and have to solve sets of linear equations. The following are the equations.

4x-9y=0
3x+2y=35

I try to add them:
7x-7y=35

Then I'm stuck. I just don't get it. Am I even on the right track by beginning this way? How do I remove the x or the y? Do I add 7y to both sides? Do I subtract 7x to both sides? How do I isolate x or y?

Continuing from your effort:

4x-9y=0 ............................................(1)
3x+2y=35............................................(2)

7x-7y=35 .............................................(3)...........................remember that (3) is not independent

7x-7y=35 ........→......... x - y = 5 ......... →....... x = y + 5 ...........(4)

replace 'x' from (4) into (1)

4*(y + 5) - 9y = 0 ........→...... 20 - 5y = 0 ..... → y = 4 ...............(5)

Use this value of 'y' into (4) and calculate 'x'

Now use the calculated values of 'x' and 'y' into (1) and (2), to confirm the answers.

Note that there are many different (correct) paths to get to the (correct) answer. You will choose the most convenient path for you.

 

[HallsofIvy]

Brief bg. Im in my 40's attempting to pass the gmat exam. I have never and I mean never understood algebra. I can code software and completely rebuild motors, but I cannot understand algebra. Please help!

I am taking a self learning algebra course online and have to solve sets of linear equations. The following are the equations.

4x-9y=0
3x+2y=35

I try to add them:
7x-7y=35

Then I'm stuck. I just don't get it. Am I even on the right track by beginning this way? How do I remove the x or the y? Do I add 7y to both sides? Do I subtract 7x to both sides? How do I isolate x or y?

WHY did you add them? Did you have some purpose? You don't solve algebra problems by doing things randomly!

If you are given problems involving "two equation in two unknowns" then you must have already dealt with "one equation in one unknown" and the basic rule is to reduce to that simpler problem. (A general rule for dealing with complicated problems is "reduce it to a simpler problem.

There are many ways to do that- which is best depends on the specific problem. That requires thinking, not just memorizing rules!

We have 4x- 9y= 0 and 3x+ 2y= 35.

One way- I see that one equation has "-9y" and the other has "2y". If I multiply the first by 2 and the second by 9 I will have "-18y" and "18y" which will cancel:
8x- 18y= 0 and 27x+ 18y= 315.
Adding the two equations eliminates y and leaves
35x= 315.

Dividing both sides by 35, x= 315/35= 9.
Now 4x- 9y= 36- 9y= 0. Adding 9y to both sides, 36= 9y.
Dividing both sides by 9, y= 4.

Check: with x= 9, y= 4, 4x- 9y= 4(9)- 9(4)= 36- 36= 0 and 3x+ 2y= 3(9)+ 2(4)= 27+ 8= 35.

Another way- one equation has "4x" and the other has "3x". If I multiply the first equation by 3 and the second equation by 4, I have 12x- 27y= 0 and 12x+ 8y= 140. Subtracting the first equation from the second equation eliminates x: 8y- (-27)y= 35y= 140. y= 140/35= 4. Then 4x- 9y= 4x- 36= 0, 4x= 36, x= 9, as before.

A third way, from 4x- 9y= 0, 4x= 9y so y= (4/9)x. Then 3x+ 2y= 3x+ 2(4/9)x= 3x+ (8/9)x= (27+ 8)x/9= 35. 35x= 9(35) so x= 9. Putting x= 9 in either of the equations gives y= 4 as before.

The point is that algebra is NOT just memorizing and applying formulas, it is about thinking!

You want to simplify the equations. Don't just "do things" (like adding the two equations) at random. You have to have a reason for every step.