(Solved) How do you solve using the elimination method? 3r-2s=6 and 2r+3s=43?

First of all write down the two equations you have given and number each one of them :

3r - 2s = 6 (1)

2r + 3s = 43 (2)

We could choose to eliminate either the variable r or the variable s.

But let us decide that s is the variable we will eliminate in order to solve the simultaneous equations you have given in your question.

In order to eliminate s we must get the coefficient of s in equation (1)and equation (2) the same. In this case our intention should be to get the coefficient of s in both equations up to 6.

To do this multiply equation (1) by 3 and equation (2) by 2. The equations then become :

9r - 6s = 18 (3)

4r + 6s = 86 (4)

Now that the coefficients of s are equal in both of the equations and the fact that the signs are opposite (-6 and +6) you will need to ADD equation (3) and equation (4) together to eliminate s. Doing so gives :

13r = 104
r = 8

We could use any of equations (1), (2), (3) or (4) in order to obtain the value of variable s.

But I am going to use equation (2) for this purpose. Inserting r = 8 into equation (2) gives :

2(8) + 3s = 43
16 + 3s = 43
3s = 43 - 16
3s = 27
s = 9

so the solution of the simultaneous equations you gave in your question is

(r = 8, s = 9)

Hope this answered your question.

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How do you solve using the elimination method? 3r-2s=6 and 2r+3s=43?

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