Question

How do you solve the system of equations `4y = 9x - 17` and `9x - 6y = 3`?

Answer 1

`x=5 and y=7`

Explanation:

Both equations have the same term in `x`.

To eliminate the `x` term, you could subtract the equations,
However, here is another option:

Isolate the `9x` term in each equation.

`color(blue)(9x = 6y+3)" " and" "color(red)(9x =4y+17`

`color(white)(wwwwwwwww.)color(blue)(9x) =color(red)(9x)`

therefore the two right hand sides are also equal

Equate them: `" "color(blue)(6y+3) = color(red)(4y+17`

`color(white)(wwwwwwwww.)6y-4y =17-3`

`color(white)(wwwwwww.wwww.)2y = 14`

`color(white)(w.......www.wwwww.)y=7`

Substitute `7` for `y` to find the value of `x`

`color(white)(wwwwwwwww.)9x = 6(7) +3`

`color(white)(wwwwwwwww.)9x = 45`

`color(white)(wwwwwww.ww.)x =5`