Algebra Help.?

Question

http://regentsprep.org/Regents/math/syslin/AlgSys.htm
. . .

I am Looking at the page linked above, trying to understand what to do here, but even though the information is presented in a simple fashion... I still have trouble "grasping" this:
3y - 2x = 11 AND
y + 2x = 9
...The site tells me to " Replace the "y" value in the first equation by what "y" now equals. "Grab the "y" value and plug it into the other equation."
....I don't understand why I am doing this, and cannot apply this to a similar, yet different problem.
Can someone please explain this to me as if I were four years old? I am relativley "smart", but this concept is eluding me.
...I am studying for my G.E.D., and I would like to thank everyone in advance for taking the time to help me in my endeavors.

Answer 1

scroll down the page, it explains how to do it.

Answer 2

Each equation stands for an equation of a line. What you are saying sounds like substitution. This is you are basically trying to find out where the two lines cross. So ...

3y - 2x = 11

y + 2x = 9 this can be rewriten as y = -2x+9

Now you know what y equals in one line, but you want to know what it equals in both lines so you replace the y in the second equation with what it equals (the -2x+9)

So 3(-2x+9) - 2x = 11
-6x+27 - 2x = 11
-8x = -16
x = 2 you take this value and put it back into the second equation to get

y + 2(2) = 9
y = 5

You just found the value of x and y that makes both equations true.

Answer 3

Well, the variable "y" seems easier to solve for the first step, so look at the equation y+2x=9 first. In order to see what "y" equals to, you need to move the "2x" to the right side of the equal sign. To do this, simply subtract "2x" from both sides of the equal sign: y+2x-2x=9-2x. After this step, you are left with y=9-2x. So, now that we know what the variable "y" equals to, simply substitute "y" into the other equation. Like so: 3(y)-2x=11 will become
3(9-2x)-2x=11. Lastly, all you have to do now is to combine "like terms", multiply, subtract, and do whatever is necessary. Like so: 3(9-2x)-2x=11...27-6x-2x=11...
27-8x=11...-8x=-16...x=2. So now, you know that x=2. To find out what "y" really equals to, you must substitute what "x" equals to into one of the equations and solve for "y". It doesn't matter which equation you use. I am going to use y+2x=9. Now, you simply "plug" in what "x" is (that would be 2) into the equation. Thus, the equation should look like this now: y+2(2)=9. Then, you just solve for the variable "y": y+2(2)=9...y+4=9...y=5. So now you know that x=2 and y=5. And your done! Hope this helps, and good luck!

Answer 4

3y-2x=11
y+2x = 9

What they're saying to do is solve the second equation for y.

y = 9-2x

Now put that in the first equation (9-2x) where you see "y."
3 (9-2x) - 2x = 11

Now solve for x
27 - 6x - 2x = 11
-8x = -16
x = 2

Now put 2 in the equation (either one) where you see "x"
y + 2 (2) = 9
y + 4 = 9
y = 5

Now put 2 and 5 in the other one to check it and make sure it's right.
3(5) - 2(2) = 11
15 -4 = 11
11 = 11. This is true, so the answer x = 2, y = 5 is correct.

Answer 5

Let's Just use addition method.It's easiest.
3y-2x=11 (1)
+ y+2x=9 (2)
______________
4y=20 , y=20/4 or y=5
remplace y in (2) equation to find x.
5+2x=9
Transp. +5 to the other side.
(it becomes -5).
2x=9-5 ; 2x=4
x=4/2 or x=2

S ={2,5}
GOOD LUCK !

Answer 6

Replace y with 0, then solve for x. When you found the value of x you can plug that into the original eq. and solve for y.