Equations

[HNO]

Solve this system of equations: I have not done these question since last year so I need a bit of reviewing

3x - 4y = 18
-2x + y = -7

I collected like terms

1 x + -3y + 11

or I got

x + -3y - 11

5x - 5y - 11

…are any of these correct? I'm most certain about second answer I got

 

[Deleted member 4993]

Solve this system of equations: I have not done these question since last year so I need a bit of reviewing

3x - 4y = 18
-2x + y = -7

I collected like terms

1 x + -3y + 11 <<<<<<<<<<<<<<<<<< Incorrect and does not make sense - where did the "equal-to" sign go?

or I got

x + -3y - 11

5x - 5y - 11

…are any of these correct? I'm most certain about second answer I got

For a quick review of solution process - go to:

http://www.purplemath.com/modules/systlin1.htm

 

[HNO]

For a quick review of solution process - go to:

http://www.purplemath.com/modules/systlin1.htm

Is x + -3y - 11= 0 incorrect?

 

[JeffM]

Is x + -3y - 11= 0 incorrect?

It is not incorrect; it is just useless as an answer to the problem assigned.

You are asked to SOLVE the system of equations, which means to find the numeric values of x and y for which the two equations are simultanously true.

Subhotosh Khan gave you a reference on how to solve systems of two equations in two unknowns. You need to review it.

 

[HallsofIvy]

Solve this system of equations: I have not done these question since last year so I need a bit of reviewing

3x - 4y = 18
-2x + y = -7

I collected like terms

The point is NOT to "collect like terms" but to eliminate one of the unknown values.
If you multiply the first equation by 2, you get 6x- 4y= 36. If you multiply the second equation by 3 you get -6x+ 3y= -21.
Now what do you get if you add those two equations?

Another way to "eliminate" a value is to solve one equation for one in terms of the other: 3x- 4y= 18 is the same as 3x= 4y+ 18 and then, dividing both sides by 3, x= (4/3)y+6. Now you can replace x in the second equation by (4/3)y+ 6 changing it to -2((4/3)y+ 6)+ y= -7, an equation in y only.

 

[HNO]

The point is NOT to "collect like terms" but to eliminate one of the unknown values.
If you multiply the first equation by 2, you get 6x- 4y= 36. If you multiply the second equation by 3 you get -6x+ 3y= -21.
Now what do you get if you add those two equations?

Another way to "eliminate" a value is to solve one equation for one in terms of the other: 3x- 4y= 18 is the same as 3x= 4y+ 18 and then, dividing both sides by 3, x= (4/3)y+6. Now you can replace x in the second equation by (4/3)y+ 6 changing it to -2((4/3)y+ 6)+ y= -7, an equation in y only.

Why would I multiply the equation by 3 and 2??? can I not just add them right away then ?

3x - 4y = 18 > 3x -4y -18
-2x + y = -7> -2x + y + 7

3 + -2= 1x

-4 + 1= -3y

-18 + 7= -11

so would that not be x + -3y -11?

Sorry I'm so confused its been a while since I have done these

 

[HNO]

Why would I multiply the equation by 3 and 2??? can I not just add them right away then ?

3x - 4y = 18 > 3x -4y -18
-2x + y = -7> -2x + y + 7

3 + -2= 1x

-4 + 1= -3y

-18 + 7= -11

so would that not be x + -3y -11?

Sorry I'm so confused its been a while since I have done these

I was just reading and I saw another comment … I'm actually solving everything wrong .. am I actually looking for x and y value?

 

[HNO]

I did everything and it seems that it works as after I plugged x + y into my equation and it works but it might still be wrong.

I got x= 2
I got y= -3

If someone has done this question and got the same answer please inform me!

THANKS FOR ALL YOUR HELP !! ;-) HNO

 

[JeffM]

I did everything and it seems that it works as after I plugged x + y into my equation and it works but it might still be wrong.

I got x= 2
I got y= -3

If someone has done this question and got the same answer please inform me!

THANKS FOR ALL YOUR HELP !! ;-) HNO

Well the answer is correct as you can tell by putting the values into the two equations

\(\displaystyle 3(2) -(4)(-3) = 6 + 12 = 18\ and\ -2(2) + (-3) = - 4 - 3 = -7.\)

But it is quite unclear how you got the answer. Again, I suggest that you look at the review suggested by SK so that you can do these problems on a test without help.

 

[HNO]

Well the answer is correct as you can tell by putting the values into the two equations

\(\displaystyle 3(2) -(4)(-3) = 6 + 12 = 18\ and\ -2(2) + (-3) = - 4 - 3 = -7.\)

But it is quite unclear how you got the answer. Again, I suggest that you look at the review suggested by SK so that you can do these problems on a test without help.

I did look at the reviews and I was in a rush to get to dance … so I just decided to write what I got… I understand now thanks guys for all your help (=