simultaneous equation;?

Question

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

work out this equation and show your answer

(I already know the answer, x=4, y=1, im having difficulty in how you get to this asnwer. Usually i would double one of the answers to get rid of an 'x' or a 'y', but as there are is only 1 'x' and 1 'y' im unsure how you do it. any help, and no smart asses please, just answer the question.

Answer 1

Even though there is only one x in the top equation, you can still just double it, as follows:

2x + 6y = 14

Now we will subtract the second equation from this (keep in mind you're subtracting a negative y, so it ends up being addition):

2x + 6y = 14
- 2x - y = 7
________________

7y = 7

After dividing by 7 on each side, you get:

y = 1

Now, plug this into either equation (I'll just use the second one):

2x - y = 7
2x - 1 = 7

Now, add 1 to each side:

2x = 8

After dividing by 2 on each side, you get:

x = 4

Therefore, we have x = 4, y = 1.

Answer 2

Avoid subtracting negative terms if possible, it often leads to errors. You have a positive y term in one equation and a negative term in the other. This is the one to eliminate.
Multiply the second equation by 3.
This gives 6x - 3y= 21
The other equation is x+ 3y = 7
Add the two equations 7x = 28 (since -3y + 3y =0)
So x = 4
Substitute x= 4 in the first equation

This gives 4 +3y = 7 so y is obviously 1

You can check this is right in the second equation

2x - y =2 x 4 - 1 =7 which is true.

Answer 3

x+3y=7 x+3y=7
2x- y=7 myltiply by 3 6x -3y = 21

add the two equations 7x = 28 divide by 7
x = 4

substitute in first eq 4 + 3y = 7
3y = 7 - 4
3y = 3 divide by 3
y = 1

x = 4 and y = 1

Answer 4

Well, there are two ways to solve it, elimination and substitution. In this case, it is probably easiest to do substitution because you have some variables already without coefficients. However, you mentioned trying elimination instead, so I'll show you that way.

Even though there is only one x in the top equation, you can still just double it, as follows:

2x + 6y = 14

Now we will subtract the second equation from this (keep in mind you're subtracting a negative y, so it ends up being addition):

2x + 6y = 14
- 2x - y = 7
________________

7y = 7

After dividing by 7 on each side, you get:

y = 1

Now, plug this into either equation (I'll just use the second one):

2x - y = 7
2x - 1 = 7

Now, add 1 to each side:

2x = 8

After dividing by 2 on each side, you get:

x = 4

Therefore, we have x = 4, y = 1.

Answer 5

first you need to make one thing the same. I would reccommend making both X's the same number. so make both of the 2x. You all ready of an equation with 2x but the other only has one x. multiply that equation by -2 so that the equations cancel one another out. you should end up like this.
-2x-6y=-14
2x-y=7
by cancelling them out you are left with this -6y=-14 and -y=7. Add the two together to equal -7y= -7 which means that y=1.
from there you need to substitue y in one equation. use the equation x+3y=7 because there is 3y and y=1 1x3=3. to find x minus 3 from 7 which gives you 4. so x=4 and y=1

Answer 6

Strangely enough, nobody has come out with the most simple solution of all. Since both equations equal 7, they must both be equal to each other. So:

x + 3y = 2x - y.

Taking away x from both sides and adding y to both sides leaves us with:

4y = x
If we now substitute 4y into the first equation we get:

4y + 3y = 7 or 7y = 7. So y = 1.

The rest of course, is straight forward.

Answer 7

x + 3y = 7- - - - - - Equation 1
2x - y = 7- - - - - - -Equation 2
- - - - - - - - - -

Multiply equation 2 by 3

2x - y = 7

3(2x) - 3(y) = 3(7)

6x - 3y = 21

- - - - - - - - - -

x + 3y = 7
6x - 3y = 21
- - - - - - - - - -
7x = 28

7x / 7 = 28 / 7

x = 28/7

x = 4

Insert the x value into equation 1
- - - - - - - - - - -

x + 3y = 7

4 + 3y = 7

4 + 3y - 4 = 7 - 4

3y = 3

3y / 3 = 3/3

y = 3/3

y = 1

Insert the y value into equation 1
- - - - - - - -

Check equation 1

x + 3y = 7

4 + 3(1) = 7

3 + 3 = 7

7 = 7

- - - - - - - -

Check equation 2

2x - y = 7

2(4) - 1 = 7

8 - 1 = 7

7 = 7

- - - - - - - -

Both equations balance

The solution set { 4, 1 }

- - - - - - - - - -s-

Answer 8

x+3y=7
2x- y=7
so : x+3y=2x-y ====> 4y=x
now replace x with 4y in one of the equations ( there is no difference)

i choose first equation so:
4y+3y=7 =====> 7y=7 ====> y=1
you had from first line 4y=x so x=4*1=4

so y=1 x=4

Answer 9

Isolate "x" or "y" in either equation. Let's isolate "x" in the 1st equation.

First: subtract 3y from both sides (when you move a term to the opposite side, always use the opposite sign).

x + 3y-3y = 7-3y
x = 7 - 3y

Sec: replace/substitute 7-3y with "x" in the 2nd equation.

2(7-3y) - y = 7
2(7)+2(-3y) - y = 7
14 - 6y - y = 7
14 - 7y = 7 (subtract 14 from both sides).
14 -14- 7y = 7-14
- 7y = -7 (divide both sides by -7).
- 7y/-7 = -7/-7
y = 1

Third: replace/substitute 1 with "y" in the 1st equation.

x + 3(1) = 7
x+3 = 7 (subtract 3 from both sides).
x+3-3 = 7-3
x = 7-3
x = 4

Solution Set: (4, 1)

Answer 10

well im afraid im going to have to make a smart *** remark: whats wrong with doubling the first equation in the way you normally do it? I f you do that, you get 2x+3y=14 and then you minus equation 2 from it. this gives you the y value, which you then substitute to solve for x.