Question

How do you solve the following system?: `x - 3y = 0 , 3x + y = 7`

Answer 1

`x=21/10` and `y=7/10`

Explanation:

`x-3y=0`
`3x+y=7`

Let's solve for `x` in the first equation so we can use substitution

`x=3y`

Now plug that into the second equation

`3(3y)+y=7`

`9y+y=7`

`10y=7`

`y=7/10`

Plug that back into the first equation:

`x=3(7/10)`

`x=21/10`

`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .`

To check our work, let's substitute `21/10` and `7/10` for `x` and `y` and solve. If we get the same answer as the equation, we are correct

`3x+y=7`

`3(21/10)+(7/10)` should equal `7`

`63/10+7/10`

`70/10`

`7` equals `7`

We were right!