Question

How do you solve the following system: `6x + y = 2, 4x + 7y = 6x`?

Answer 1

`(7/22, 1/11)`

Explanation:

In order to solve systems of linear equations, you must first simplify your equations (combine all terms in the equation with the same variable).

`6x + y = 2`
`4x + 7y = 6x`

[Simplifying the 2nd equation]
`4x + 7y = 6x`
`2x - 7y = 0`

Now, you can choose whether to use the substitution method or elimination. Its up to you to choose which one you are more comfortable with but for now I will be using substitution since the `y` variable in the 1st equation has a coefficient of 1.

[Rearranging 1st Eqtn to isolate `y`]
`6x + y = 2`
`y = 2 - 6x`

[Substituting it to the 2nd equation]
`2x - 7y = 0`
`2x - 7(2 - 6x) = 0`
`2x - 14 + 42x = 0`
`44x - 14 = 0`
`44x = 14`
`x = 14/44`
`x = 7/22`

[Solving for `y`]
`y = 2 - 6(7/22)`
`y = 2 - 21/11`
`y = 1/11`

So the final answer is `(7/22, 1/11)`