2r+3t=9

3r+2t=12

(Use Elimination)

Solve?

r = 3          and    t =  3/5

Step-by-step explanation:

2r+3t=9   ------------------------------------------------(1)

3r+2t=12 ------------------------------------------------(2)

We will first eliminate r, to so that, multiply equation (1) by 3 and multiply equation (2) by 2

6r + 9t =27 -----------------------------------------------(3)

6r + 4t = 24-----------------------------------------------(4)

subtract equation (4) from equation (3)

5t = 3

Divide both-side of the equation by 5

5t/5 = 3/5

t =  3/5

We will now proceed to eliminate t from equation (1) and (2)

To do that, multiply equation (1) by 2  and multiply equation (2) by 3

4r + 6t = 18 ------------------------------------(5)

9r + 6t =36 -------------------------------------(6)

Subtract equation (6) from equation (5)

-5r = - 18

Divide both-side of the equation by -5

-5r/-5  = -18/-5

r = 3

Therefore r = 3   and    t =  3/5

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