Question

Solve the following system of equations below x-2y=3 2x-3y=9

Answer 1

`x - 2y = 3 \\ 2x - 3y = 9 \\ \\ - 2x + 4y = - 12 \\ \: 2x - 3y = 9 \\ \\ y = - 3 \\ 2x + 9 = 9 \\ 2x = 0 \\ x = 0 \\ x = 0 \: \: y = - 3`

Answer 2

(9, 3)

Explanation:

I'd strongly suggest that you write these two equations one above the other:

x-2y=3

2x-3y=9

Let's eliminate x by addition / subtraction: Multiply the first equation by -2 to obtain -2x in the first row over +2x in the second row:

-2x + 4y = -6

2x - 3y = 9

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y = 3

Now subst. 3 for y in the first equation: x - 2y = 3 becomes:

x - 2(3) = 3, or

x = 6 + 3 = 9

The solution is (9, 3).