Question

How would you solve the system of these two linear equations: `2x + 3y = -1` and `x - 2y = 3`? Enter your solution as an ordered pair (x,y).

Answer 1

`(1, -1)`

Explanation:

Given,

`{(2x + 3y = -1 color(white)(xxxxxx) "---(I)"), (x - 2y = 3 color(white)(xxxxxxxxx) "---(II)") :}`

Multiply `"(II)"` by `2` and then subtract from `"(I)"`,

`7y = -7`
`color(white)(x)y = -1`

Putting `y = -1` in `"(I)"`,

`2x + 3(-1) = -1`

`color(white)(xxxxxxx) 2x = -1 + 3`

`color(white)(xxxxxxx) 2x = 2`

`color(white)(xxxxxxxx) x = 1`.

Hence, `x = 1` and `y = -1`