Question

How do you solve 5x+6y=24 and 3x+5y=18?

Answer 1

`{(x = 12/7), (y = 18/7) :}`

Explanation:

Your starting system of equations is

`{(5x + 6y = 24), (3x + 5y = 18):}`

Multiply the first equation by `(-3)` and the second equation by `5` to get

`{(5x + 6y = 24| * (-3)), (3x + 5y = 18| * 5):}`

`{(-15x - 18y = -72), (15x + 25y = 90):}`

Notice that if you add these two equations, more specifically if you add the left-hand sides and the right-hand sides separately, you can eliminate the `x`-term.

This will allow you to solve the resulting equation for `y`

`{(-15x - 18y = -72), (15x + 25y = 90):}`
`stackrel("-------------------------------------------------------")`
`color(red)(cancel(color(black)(15x))) - 18y + color(red)(cancel(color(black)(15x))) + 25y = -72 + 90`

`7y = 18 implies y = color(green)(18/7)`

Now use this value of `y` in one of the two original equations to get the value of `x`

`5x + 6 * 18/7 = 24`

`35x + 108 = 168`

`35x = 60 implies x = color(green)(12/7)`