Question

How do you solve the system : `2x+6y=5`, `8x+24y=20`?

Answer 1

Infinitely many solutions

Explanation:

Hello there!

`2x + 6y = 5`
`8x + 24y = 20`

You can solve the system by using the elimination form or you can use the substitution form. I like substitution so I'll use it :)

We need to solve `2x + 6y = 5` for x
`2x + 6y = 5`
`2x = -6y + 5`
Divide both sides by 2
`(2x)/2` = `(-6y+5)/2`
`x` = `-3y` +`5/2`
Now substitute `-3y` +`5/2` for `x` in `8x +24y = 20`
`8` `(-3y + 5/2)` + `24y = 20`
Distribute
`(8)(-3y) + (8)(5/2) + 24y = 20`
`-24y + 20 + 24y_ = 20`
`20 = 20`
Add -20 to both sides
`20 - 20 = 20 - 20`
`0 = 0`
Final answer: All real numbers are solutions

I hope I helped!