Here's another x, y?

Question

I never know how to do these kind of problems with the one y

3x - 2y = -12
-5x - y = 7

Thank you sooooooooo much :)

Answer 1

3x-2y=-12
-10x-2y=14
subtracting
13x=-26
sdividing by 13
x=-2
sub in (1)
3(-2)-2y=-12
-6-2y=-12
adding 6
-2y=-6
dividing by -2
y=3
solution {-2,3}

Answer 2

There are two methods to solve - you pick one - don't mix both

method 1: By Substitution
pick one equation and solve for Y then plug into the other equation:

3x - 2y = -12
-5x -y = 7 <-- will use this to solve for y and plug into top one:

y = -5x - 7
plug in: 3x - 2(-5x - 7) = -12 combine like terms and solve. Leave that up to you.

Method 2: This is refered by many names ( Elimination, by addition or by subtraction) Basically pick a variable to eliminate, say Y. You'll have to make y's on both equation the same, notice -2y on the first therefore i need a -2 on the second for -y to cancel the negative

-2(-5x -y = 7) come to 10x +2y = -14 <- new eq.

add both now
3x -2y = -12
10x +2y = -14
-------------------
13x = -26
solve for x
x = -2
now since you have x plug into any other equation and solve y and your done.
I'll pick the first:
3(-2) - 2y = -12
-6 -2y = -12
-2y = -6
y = 3;
Therefore X = -2 Y = 3

Answer 3

Elimination by adition Method

3x - 2y = - 12 - - - - - Equation 1
- 5x - y = 7- - - - - - - Equation 2
- - - - - - - - - - -
Multiply equation 2 by - 2

-5 - y = 7

-2(- 5x) - 2(- y) = -2(7)

10x + 2y = -14 New equation 2
- - - - - - - - - - -

Elimination of y and solving for x

3x - 2y = - 12
10x + 2y = - 14
- - - - - - - - - -
13x = - 26

13x/13 = - 26/16

x = - 2

The answer is x = - 2

Insert the x value into equation 2

- - - - - - - - - - - - - - - - - - - - - -

Solving for y

- 5x - y = 7

- 5(- 2) - y = 7

10 - y = 7

10 - y - 10 = 7 - 10

- y = - 3

- 1(- y ) = - 1(- 3)

y = 3

The answer is y = 3

Insert the y value into equation 2

- - - - - - - - - - - - - - - - - - - - - -

Check for equation 2

-5x - y = 7

- 5(- 2) - (3) = 7

10 - 3 = 7

7 = 7

- - - - - - - - - - - - - - -

Check for equation 1

3x - 2y = - 12

3( - 2) - 2(3) = - 12

-3 - 6 = - 12

- 12 = - 12

- - - - - - - - - - - -

The solution set is { - 2, 3 }

- - - - - - -s-

Answer 4

Solve to get y:

-y = 7 + 5x

y = -7 - 5x

Plug y in

3x - 2(-7 - 5x) = -12

3x + 14 + 10x = -12

13x + 14 = -12

13x = -26

x = -26/13

x = -2

Plug it back into one of the originals and solve for y again

-5(-2) - y = 7

10 - y = 7

-y = -3

y = 3


Answer:
x = -2 y = 3

Answer 5

3x-2y = -12
-5x - y = 7
Multiply the 2nd equation by -2 to get:
10x +2y =-14
Now add this new equation to the first equation getting:
13x=-26
x= -2
Now substitut x = -2 into the the second equation to get:
-5(-2) -y =7
10 - y =7
10 -7 =y
3 = y

Answer 6

3x-2y=-12.................say eqn1
-5x-y=7......................say eqn2
in such kind of problems u have to eliminate one term either x or y..
multiplyin eqn 2 by 2 ..we will get 2y and then subtracting eqn 1 and eqn 2 y will get cancelled.....
3x-2y=-12......eqn 1
eqn 2 after multiplyin by 2 bcoms..
-10x-2y=14......eqn2
subtracting 1 and 2....
3x-2y=-12
10x+2y=-14
we will get y cancelled n finaly .....13x=-26 or x=-2
putting value of x in ne eqn say 2...
-5x-y=7
-5*-2-y=7
10-y=7
y=3

Answer 7

3x - 2y= -12
-5x - y=7

8x - y= -19
=19+8x -y
y=19+8x

-5x - 19 -8x=7
-13 x=26
x= - 2
y=37

Answer 8

3x-2y=-12
-5x-y=7 || *(-2)
-----------------
3x-2y=-12
+ 10x+2y=-14
----------------------
13x=-26 || :13
x=-2

3*(-2)-2y=-12
-2y=-6 ||:(-2)
y=3

Answer 9

3x-2y=-12
-10x-2y=14
---------------
13x=-26
x=-2
plug that in...
3(-2)-2y=-12
-6-2y=-12
-2y=-6
y=3

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

Answer 10

(-2,3)