Question

How do you solve the simultaneous equations `3x + 5y = 11` and `2x + y = 3`?

Answer 1

I found:
`x=4/7`
`y=13/7`

Explanation:

From the second equation you can isolate `y` as:
`y=3-2x`
substitute nto the first to find `x`:
`3x+5(color(red)(3-2x))=11`
`3x+15-10x=11`
`-7x=-4`
`x=4/7`
substitute back into the second equation:
`y=3-2(4/7)=(21-8)/7=13/7`

Answer 2

`(x,y) = (4/7, 13/7)`

Explanation:

[1]`color(white)("XXXX")` `3x+5y = 11`
[2]`color(white)("XXXX")` `2x+y = 3`

subtract `2x` from both sides of [2] to isolate `y` on the left side
[3]`color(white)("XXXX")` `y = 3-2x`

substitute `(3-2x)` for `y` in [1]
[4]`color(white)("XXXX")` `3x + 5(3-2x) = 11`

simplify
[5]`color(white)("XXXX")` `-7x + 15 = 11`

[6]`color(white)("XXXX")` `x = 4/7`

substituting `4/7` for `x` in [2]
[7]`color(white)("XXXX")` `2(4/7) + y = 3`

[8]`color(white)("XXXX")` `y = 13/7`