We draw the 2 lines as follows.

2x + 3y = 5 is in green.

x − 3y = 7 is in magenta.

1 2 3 4 5 6 7 8 9 -1 -2 -3 -4 1 2 3 -1 -2 -3 -4 -5 x y
`x-3y=7`
`2x+3y=5`

Graphs of `y = (-2x-5)/3` and `y=(x+7)/3`.

We observe that the point (4,−1) is on both lines on the graph. We say (4,−1) is the solution for the set of simultaneous equations.

This means the solutions are `x = 4`, `y =-1`.

Notice that these values are true in both equations, as follows.

2(4) + 3(−1) = 8 − 3 = 5 [OK]

(4) − 3(−1) = 4 + 3 = 7 [OK]

So we see the intersection point of the 2 lines does give us the solution for the system.

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