Elimination method?

2r - 3s = -3
3r + 2s = 28

2r - 3s = -3
3(2r - 3s) = 3(-3)
6r - 9s = -9

3r + 2s = 28
2(3r + 2s) = 2(28)
6r + 4s = 56

...6r - 9s = -9
-- 6r + 4s = 56 (subtraction)
---------------------
-13s = -65

-13s = -65
s = -65/-13
s = 5

2r - 3s = -3
2r - 3(5) = -3
2r - 15 = -3
2r = -3 + 15
2r = 12
r = 12/2
r = 6

∴ r = 6 , s = 5

4r - 6s = - 6
9r + 6s = 84----------Add

13r = 78
r = 6

18 + 2s = 28
2s = 10
s = 5

r = 6 , s = 5

2r - 3s = -3
3r + 2s = 28
(i'm going to multiply the top by -3 and the bottom by 2)
-3(2r - 3s) = -3(-3)
2(3r+2s) = 2(28)
(simplify)
-6r + 9s = 9
6r +4s = 56
(subtract down and eliminate r)
5s = -47
(divide by 5)
s = -9.4
(substitute s into one of the original problems)
3r + 2(-9.4) = 28
(simplify)
3r - 18.8 = 28
(add 18.8 to both sides)
3r = 46.8
(divide by 3)
r = 15.6

answer: r = 15.6 and s = -9.4

Elimation method means elimate one variable from the given equations. In this case, you have 2 variables, r and s and 2 equations. If you have 2 variables and only one equation, you cannot solve it. Possible trick question in the test.

In any case, try to analyze first. By looking at the given, note that you can ELIMINATE the variable s better than r because one is negative already and all you have to do is multiply -3s by 2 and +2s by three. Also this results in addition rather than subtraction. Thus you get,

4r -6s = -6
9r +6s = 84

then eliminating 6s, you get 13r = 78. Divide by 13, you get r= 6

Now to find s, try to analyze again instead of just plugging away. Addition is always easier than subtraction, so use second equation to plug r=6, Also the sign in front of s variable is positive so less chance for errors, (note: most algebra errors are with wrong signs)


You get, 3(6) +2s = 28, you will find s =5.

There are many ways of solving systems of linear equations, but it always help exactly what is meant by ELIMINATION method.

Multiply the top by 3 to get
6r-9s=-9.
Multiply the bottom by 2 to get
6r+4s=56

Subtract top from bottom to get
6r-6r +4s--9s=65
0+13s=65
s=65/13=5
Plug this value back in:
2r-3(65/13)=-3
2r=-3+(195/13)
2r=156/13
r=78/13=6

Check: 3*(6)+2*(5)=18+10=28

I do not know,I haven't been practicing.