We can write the answers using coordinates like the following.

First student's answer: `(1, 4)`.

Second student's answer: `(1/3,2).`

If `(1, 4)` satisfies both equations, then it is the correct answer.

Test in first equation:

`−3(1) + 4 = −3 + 4 = 1` [OK]

Test in second equation:

`6(1) − 3(4) = 6 − 12 = −6` [Not OK, should be `−4`]

Since the first answer doesn't work in both equations, we conclude it is not the correct solution.


Let's now try the second student's solution.

If `(1/3,2)` satisfies both equations, then it is a solution of the system.

By substitution:

Test in first equation:

`−3(1/3) + 2 = −1 + 2 = 1` [OK]

Test in second equation:

`6(1/3) − 3(2)= 2 − 6 = −4` [OK]

So we conclude the second student had the correct solution to the set of simultaneous equations, `(1/3,2).`

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