Question

What are the solution(s) of the system of equations 2x+y=1, x-y=3?

Answer 1

`{(x = 4/3), (y = -5/3) :}`

Explanation:

Your system of equations looks like this

`{(2x + y = 1), (x - y = 3) :}`

Notice that if you add the left-hand sides and the right-hand sides of the two equations separately, the `y`-term will cancel out. This will allow you to find the value of `x`.

`{(2x + y = 1), (x - y = 3) :}`
`color(white)(x)stackrel("----------------------------")`

`2x + color(red)(cancel(color(black)(y))) + x - color(red)(cancel(color(black)(y))) = 1 + 3`

`3x = 4 implies x= color(green)(4/3)`

Pick one of the two equations and replace `x` with its determined value to get the value of `y`.

`4/3 - y = 3`

`4 - 3y = 9`

`-3y = 5 implies y = color(green)(-5/3)`

Therefore, the solution set for this system of equations is

`{(x=4/3), (y = -5/3) :}`