Question

How do you solve `2x+7y=10` and `x-2y=15`?

Answer 1

`{(x = 125/11), (y = -20/11) :}`

Explanation:

You could solve this sytem of equations by multiplication.

More specifically, you can multiply the second equation by `-2` to get

`-2 * (x - 2y) = -2 * 15`

`-2x + 4y = -30`

The two equations now look like this

`{(2x + 7y = 10), (-2x + 4y = -30) :}`

Next, add the left side and the right side of the equations separately to cancel out the `x`-term

`color(red)cancelcolor(black)(2x) + 7y - color(red)cancelcolor(black)(2x) + 4y = 10 + (-30)`

`11y = -20 implies y = color(green)(-20/11)`

Now take this value of `y` and use it in the first equation to find the value of `x`

`2x + 7 * (-20)/11 = 10`

`2x = 10 + 140/11`

`2x = 250/11 implies x = 250/11 * 1/2 = color(green)(125/11)`