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
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

Use the 2nd equation to express y = f(x)
y = -2x + 9

Replace in first equation

3(-2x+9) - 2x = 11
-6x + 27 - 2x = 11
-8x = -16
x =2

Then y = 5

Answer 2

When you have 2 equations like that together they are trying to say that these 2 equations will be true for 1 unique value of y and 1 unique value of x. Since there can be only 1 possible value of x or y, you can solve one equation for say 'y' in this case. Take the second equation and solve it for y, you get y = 9 - 2x. Now you can use this value to solve the other equation like this -
3y - 2x = 11
=> 3(9 - 2x) - 2x = 11 (Replace y with it's value from the previous equation)
=>27 - 6x - 2x = 11
=>27 - 8x = 11
=>-8x = 11 - 27
=>-8x = -16
=> x = 2
Now we know y = 9 - 2x, so let's substitute value of x that we just calculated in there -
y = 9 - 2*2
=> y = 9 - 4
=> y = 5

Now you have x = 2 and y = 5. If you substitute these values into the 2 original equations you will see they are the only values that can give you 11 or 9 respectively.

hope this helps

Answer 3

For the question you listed above:

Your second equation is y + 2x = 9. To get anywhere, you must solve for y. Subtract 2x from both sides:

y = 9 - 2x

Now that you have a y-value, plug that (9 - 2x) into your first equation and solve for x:

3(9 - 2x) - 2x = 11

To start, distribute the three to the 9 and the 2x:

27 - 6x - 2x = 11
(3 times 9 = 27, and 3 times 2 = 6)

Now subtract like terms. In this case, it's the 6x and the 2x:

27 - 8x = 11
(-6x - 2x = -8x)

Now move the numbers without variables to the same side by subtracting 27 from both sides:

-8x = -16
(11 - 27 = -16)

To get x by itself, divide out your -8:

x = 2
(-16 divided by -8 = 2)

Now that you have x, go back to your second equation, which you rewrote as y = 9 - 2x. Plug in the x that you just found and solve for y:

y = 9 - 2(2)
y = 9 - 4
y = 5

Good luck with this; it's not too hard once you get the hang of it, but after a while it gets time-consuming. Make sure you check your work often; the longer you do it, the more careless you get.

Answer 4

You have the following equations:

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

You can't solve for two variables at the same time (meaning you can't get both x and y at once).

First, you have to get one of them "by itself":

We'll take y +2x = 9 and subtract 2x from both sides. This leaves us with:

y = -2x + 9

Now, we can take the first equation: 3y -2x = 11 and pull out the y and replace them with what we just made y equal:

3 (-2x +9) - 2x =11

Now we've gotten rid of y completely, and we can solve for x:

3 (-2x +9) - 2x =11

(Distribute the 3)
-6x + 27 - 2x = 11

(Combine the x's)
-8x + 27 = 11

(Subtract 27)
-8x = -16

(Divide by 8)
x = 2

Now, you can plug the x into one of the first equations from the very beginning:

y + 2x =9
y + 2(2) = 9
y + 4 = 9
y = 5

Now you know that x = 2, and y = 5.

You can check this by plugging them back into the original equations:

3y -2x = 11 ---> 3(5) - 2(2) = 11
y + 2x =9 ---> 5 + 2(2) = 9

Hope that helps!

Answer 5

hey .. I'll try my best to simple that ... you have two equation in two unknowns x and y there's many method to solve these equation one of them is the substation rule that you asking about .........

okay when you look to one of the equation and you want to know what is the values of x and y ... you say it's hard (not impossible - as you will study in high school lessons) .... if we look to the first equation 3y-2x=11 and we move -2x to the right side with positive sign it will be 3y=11+2x multiply the equation be 1/3 we get

y=(11+2x)/3

and we didn't get what we want also if we did the same and make 2x in one site and 3y-11 in the other side and multiply by 1/2 to remove the 2 in front of x we get

x=(3y-11)/3

we didn't have the answer yet ... okay look to the other equation

y+2x=9

if we try to get x and y it will be

x=(9-y)/3

and if we try with y

y=9-2x

okay as you see every x and y here is connected with other y and x , and we could not solve the problem if you think a little you to the last y

y=9-2x ...

look now to the first equation
3y-2x=11
we could make it equation in one variable be substituting the y of the second equation by the y in the second equation
3y-2x=11 we know that y=9-2x so
3(9-2x)-2x=11 we just substitute the y with it's value (9-2x)
27-6x-2x=11 we just multiply the 3 out the parentheses
27-8x=11 you know when adding two negative we add them with the same sing
-8x=-27+11
-8x=-16 by multiply the equation by -1/8 to get ride of the -8 in front of the x we get

x=2

i hope you could understand what i said because i know am a bad teacher .... if you understand the above you could now complete the solution

Answer 6

i think that this question is dealing with the mathematical concept, substitution. your goal is to find the point a which these lines intercect

what you need to do is first change y+2x=9 to y=-2x=9, do you understand so far?

next you put -2x+9 in the place of y in the equation 3y-2x=11, so you have only one variable in the eqation, it should look like this get an equation that looks like this,

3(-2x+9)-2x=11

then after you multiply to rid yourself of the parentheses it should look l like this

-6x+27-2x=11

i am assuming you know how to solve this but if not the next step would be to subtract 27 from 11, and then -2x from -6x

the next part of the equation looks like this,
-8x=-16
so that means that x is equal to 2, understand?

how ever you still have to find what y is equal to so plug x into the eqution y+2x=9

here is the solution

y+2x=9
y+2(2)=9
y+4=9
y=5

therfor ethe answer to this system of equations is,

the two lines intercect at 2,5

hope that helped

Answer 7

Take the one with the simplest "y" (or x). That's the second one (y is by itself; in the first one you have 3y).

Then get the y all by itself. To do that, subtract anything that's been added to it, or add anything that's been subtracted from it.

2x has been added to it. (That's what "y + 2x" means.)

Subtract 2x, and you just have y on that side of the equation.


Apply the Golden Rule of Algebra.

***Golden Rule of Algebra: You can do anything (except divide by zero) to one side of the equation as long as you do the same thing to the other side of the equation.

So you subtracted 2x from the left side, subtract 2x from the right side.

You now have y=9-2x

That's what you "grab" and plug in to the first equation where it said y:

3y - 2x = 11
3(9-2x) -2x = 11

Now simplify---first multiply (3) by (9-2x)
27-6x -2x = 11

Collect like terms--add/subtract the x's

27-8x = 11

Now it's the x you want to get on its own: subtract 27--from both sides.

-8x = 11 - 27
-8x = -16

divide both sides by -8
x=2

But you still want to know y: remember y=9 - 2x

so that means y=9-2(2)
y=9-4
y=5

Answer 8

the idea here is to use two equations, each with 2 variables, to get 1 equation with 1 variable.
solve the bottom equation for "y". this way the bottom equation now says "y=9 - 2x". Now that you know one way of describing y, you can solve the upper equation.
take 9 - 2x (which you know is one way of describing "y") and put it in place of y in the upper equation. Now you have 3(9-2x) - 2x = 11. Now, you just solve for "x".
Once you have the x value, plug it back into either of the equations and solve for "y".

Answer 9

Solve for y for one of the equations.
use that to replace the y value in the other equation.

to solve for y in the second equation, subtract 2x from both sides.
y=9-2x

substitute that into the other equation.
3(9-2x)-2x=11

now solve for x.
then substitute the x value into one of the 2 equations to get the y value.

Answer 10

basically you 2 linear equation, when you substitue one equation into the other you are eliminating either the y or x variable so you can solve for either of the two variables. Solving for the x and y variable basically gives the intercection point of the 2 linear equation.

There are two methods of eliminating one of the variables:
1)Substitution
y=9-2x
substitue into equation one
3(9-2x)-2x=11
27-6x-2x=11
27-8x=11
-8x=-16
x=2
then substitue back into equation 2
y+2(2)=9
y=9-4
y=5

solution 2) elimination
3y-2x=11
y+2x=9
add these two equation up
4y+0x=20
y=5

substitue y into either one of the equation
5+2x=9
2x=4
x=2