Real hard elimination method question?

Question

Solve by the elmination method.
8x+3y=-60
3x-3y=-39
What is the solution of the system? ________(type an ordered pair)

Answer 1

8x + 3y = - 60- - - - - - -Equation 1
3x - 3y = - 39- - - - - - - Equation 2
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11x = - 99

11x / 11 = - 99 / 11

x = - 99 / 11

x = - 9

insert the x value into equatuon 1

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8x + 3y = - 60

8(- 9) + 3y = - 60

- 72 + 3y = - 60

- 72 + 3y + 72 = - 60 + 72

3y = 12

3y / 3 = 12 / 3

y = 12 / 3

y = 4

Insert the y value into equation 1

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Check for equation 1

8x + 3y = - 60

8(- 9) + 3( 4) = - 60

- 72 + 12 = - 60

- 71 + 12 = - 60

- 60 = - 60

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Check for equation 2

3x - 3y = - 39

3(- 9) - 3(4) = - 39

- 27 - 12 = - 39

- 39 = - 39

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Both equations balance

The solution set is { -9, 4 }

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Answer 2

Elimination by addition:
Equation 1 + Equation 2 =
11x + 0y = -99
solve for x: x = -9
now plug into either equation for y:
3(-9) -3y = -39
9 + y = 13, y = 4
{x,y} : {-9, 4} ordered pair

Answer 3

8x+3y=-60
3x-3y=-39
Here, you can cancel out (+3y) and (-3y) from the 2 equations, so you get:
8x=-60
3x=-39
then, you add 8x and 3x, so you get 11x
also add (-60) and (-39) and you get (-99)
the equation now looks like this:
11x=(-99)
x=(-9)

As for the y variable, you could get it by substituting x in either of the equations. The answer is y=4
If you prefer elimination method also for y, here is how you do it:

(1) You multiply 8x+3y=(-60) by 3 and 3x-3y=(-39) by (-8) to be able to cancel out x, thus leaving y.
(2) equation one becomes 24x+9y=(-180)
equation two becomes (-24x)+24y=312
now you can cancel out 24x and (-24x), then
9y+24y= 33y ; (-180)+312 = 132
33y=132
y=4
answer: {-9,4}

If you need clarifications you can email me. I'd be glad to help ;) Good luck!

Answer 4

can't you just add both equations?

8x + 3y = -60
+ 3x - 3y = -39

= 11x = -99
x= -9

(8)(-9) + 3y = -60
-72 + 3y = -60
3y= 12
y=4

3x -3y = -39
3x-(-3)(4) = -39
3x- (-12) = -39
3x = -27
x=-9

x,y = {-9,4}

Answer 5

8x + 3y = -60 --> 1st Equation
3x - 3y = -39 --> 2nd Equation
1st + 2nd :
11x = -99
x = -9
1st*3 - 2nd*8 :
33y = 132
y = 4
x = -9, y = 4

Answer 6

8x + 3y = - 60 -----(1)
3x - 3y = - 39 ----(2)

(1) + (2) =>
11x = - 99
x = -9

(1) => 8*(-9) + 3y = - 60
3y = 12 => y = 4

(-9, 4)

Answer 7

8x + 3y = -60
3x - 3y = -39
-----------------
11x = -99
x = -11

3(-11) - 3y = -39
-33 - 3y = -39
-3y = -6
y = 2

Solution: (-11, 2)

Answer 8

Just add the equations together. The rest follows easily.