Question

What is the x-coordinate of the solution of the system `2x-3y=1` and `x+y=3`?

Answer 1

The two equations given to us are:
`2x-3y=1` -----(1)
`x+y=3` -----(2)

To find `x`, we can use the Elimination by Substitution Method
All we need to do is substitute the value of `y` from (2) in (1)
The second equation is:
`x+y=3`
Transposing `x` to the other side, we get:
`y = 3 - x`

Now we simply substitute this value of `y` in (1)
`2x-3(3-x) = 1`

`2x - 9 + 3x = 1`

`2x + 3x = 1 + 9`

`5 x = 10`

Dividing both sides by 5, we get:

`(cancel(5)x)/cancel(5) = 10/5`

`color(green)(x = 2`

The x-coordinate of the solution of the system `2x−3y=1 and x+y=3` is `color(green)(2`