Question

How do solve the following linear system?: `x-4y=2 , 2x+6y=5`?

Answer 1

`(16/7, 1/14)`

Explanation:

In order to solve systems of linear equations, you can either use the

1. Elimination Method
2. Substitution Method
3. Graphing

In this case, I would use the elimination method but note that you may use any method that you are comfortable with and still arrive at the same answer.

[Solution]
`x - 4y = 2`
`2x + 6y = 5`

Multiply 2 to both sides of the first equation...

`2x - 8y = 4`

Doing this makes the coefficient of x in the two equations the same. This enables us to subtract one equation from the other to eliminate the `x` variable

[Subtracting one equation from the other]
`2x + 6y = 5`
`2x - 8y = 4`

`14y = 1`
`y = 1/14`

Now that we know the value of `y`, we can now evaluate any of the two equations with the value of `y` to get the value of `x`

`x - 4(1/14) = 2`
`x - 2/7 = 2`
`x = 2 + 2/7`
`x = 16/7`

[Checking]
Substituting to equation 1 -> `x - 4y = 2`
`16/7 - 4(1/14) = 2`
`16/7 - 2/7 = 2`
`14/7 = 2`
`2 = 2`

Substituting to equation 2 -> `2x + 6y = 5`
`2(16/7) + 6(1/14) = 5`
`32/7 + 3/7 = 5`
`35/7 = 5`
`5 = 5`

[Final Answer]
`(16/7, 1/14)`