Question

How do you find the solution of the system of equations `3x+5y=7` and `5x+9y=7`?

Answer 1

First isolate the same term on one side of both equations.

Let us target `y`. If we multiply the first equation by `9` and the second by `5` we get:

`27x+45y=63` and `25x+45y=35`

Subtract `27x` from both sides of the first equation and `25x` from both sides of the second to get:

`45y=63-27x` and `45y=35-25x`

So `63-27x=45y=35-25x`

Ignore the `45y` in the middle and add 27x to both sides to get

`63=35+2x`

Subtract `35` from both sides to get

`28=2x`

Divide by 2 to get `x=14`

Then `45y = 35-25x = 35-25*14 = 35-350 = -315`

Divide both sides by 45 to get

`y = -315/45 = -7`

Answer 2

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