Question

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

Answer 1

`x = 6`
`y = 1`

Explanation:

We set up the two equations with 'matching' components and then use algebra to reduce the terms to a solution (if there is one).

1) `x − 4y = 2`
2) `x − 2y = 4` Subtract 1) from 2)

`2y = 2` ; `y = 1` Put this into 1) to find x:

`x − 4(1) = 2` ; `x = 6` Put this back into 2) to check for validity.

`6 − 2(1) = 4` ; `6 = 6` CORRECT!

Answer 2

`x=6, y=1`

Explanation:

`x-2y=4`

`x=2y+4`...........................eq.(1)

`x-4y=2`

`x=4y+2`...........................eq.(2)

`x=x`

eq(1)=eq(2)

`2y+4=4y+2`

`2y=2`

`y=1`

`x-2(1)=4`

`x=6`

Answer 3

`x = 6`, `y = 1`

Explanation:

`x - 4y = 2`

solve for `x`

`x = 2 + 4y`

*substitute `x` in the second equation *

`2 +4y -2y = 4`

`2 + 2y = 4`

`2y = 2`

`y = 1`

Now we solve for `x`

`x = 2 + 4(1)`

`x = 2+4`

`x = 6`

`* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *`

To double-check, let's plug in our values to the second equation

`x−2y=4`

`6 - 2(1) = 4`

`6 - 2 = 4`

`4 = 4`

We were right!