Question

How do you solve the simultaneous equations `y = 3x` and `x + 2y =21`?

Answer 1

Since we are given an expression for `y` as one of the equations, the simplest way to solve this pair of equations is through substitution.
`(x,y) = (3,9)`

Explanation:

[1]`color(white)("XXXX")` `y=3x`
[2]`color(white)("XXXX")` `x+2y = 21`

Based on [1], we can replace `y` with `3x` in [2], giving
[3]`color(white)("XXXX")` `x+2(3x) = 21`
Simplifying:
[4]`color(white)("XXXX")` `7x = 21`
or
[5]`color(white)("XXXX")` `x=3`

Based on [5], we can replace `x` with `3` in [1], giving
[6]`color(white)("XXXX")` `y = 3(3)`
or
[7]`color(white)("XXXX")` `y= 9`