We draw the 2 lines as follows.

2*x* + 3*y* = 5 is in green.

*x* − 3*y* = 7 is in magenta.

`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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