Solve by the elimination method.?

Question

Solve by the elimination method.
3r - 2s= 1
2r + 3s=31
What is the solution of the system?______
(type and ordered pair)

Answer 1

Elimination by addition method

3r - 2s = 1- - - - - - -Equation 1
2r + 3s = 31- - - - - Equation 2
- - - - - - - - - --

Multiply equation 1 by 3 and equation 2 by 2

3r - 2s = 1

3(3r) - 3(2s) = 3(1)

9r - 6s = 3

- - - - - - - - -

2r + 3s = 31

2(2r) + 2(3s) = 2(31)

4r + 6s = 62

- - - - - - - - -

Elimination of y

9x - 6s = 3
4r + 6s = 62
- - - - - - - - - -

13r = 65

13r / 13 = 65 / 13

r = 65 / 13

r = 5

Insert the r value into equation 1

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

3r - 2s = 1

3(5) - 2s = 1

15 - 2s = 1

15 - 2s - 15 = 1 - 15

- 2s = - 14

- 2s / - 2 = - 14 / - 2

s = - 14 / - 2

s = 7

Insert the s value into equation 1

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

Check for equation 1

3r - 2s = 1

3(5) - 2(7) = 1

15 - 14 = 1

1 = 1

- - - - - - -

Check for equation 2

2r + 3s = 31

2(5) + 3(7) = 31

10 + 21 = 31

31 = 31

- - - - - - - -

Both equations balance

The ordered pair (5, 7)

The solution set is { 5, 7 }

- - - - - - -s-

Answer 2

3r - 2s = 1 multiply both sides by (3)
9r - 6s = 3 -------(1)

2r + 3s = 31 multiply both sides by (2)
4r + 6s = 62 -----(2)

(1) + (2) => 13r = 65 => r = 65/13 = 5
replacing in (1) or (2)
(1) => 9*5 - 6s = 3
6s = 45 - 3 = 42 =>s = 7

Answer 3

3r - 2s= 1 --> 1st Equation
2r + 3s= 31 --> 2nd Equation

To find r,
Multiply 1st Equation by 3, and multiply 2nd Equation by 2
9r - 6s = 3
4r + 6s = 62
Make a sum of 2 Equation above, you get
13r = 65
r = 5

To find s, first, multiply 1st Equation by 2, and 2nd Equation by 3
6r - 4s= 2 --> 3rd Equation
6r + 9s= 93 --> 4th Equation
3rd-4th Equation gives
-13s = -91
s = 7
So, r = 5, s= 7

Answer 4

I would multiply the first equation by 3 and the second by two. This would let eliminate the s factor when I add them. You get:

9r-6s=3
4r+6s=62

Add them and get:

13r=65
r=5

Plug that back in and you'll have your answer.

3(5)-2s=1
15-1=2s
7=s

So r=5 and s=7.

Answer 5

s=7,r=5