Question

How do you solve y = 3x - 4 and 2x - y = 1?

Answer 1

The solution is `(x,y)=(3,5)`

Explanation:

Hence you have two linear equations we have that

`y=3x-4` and `y=2x-1`

since the first parts are equal so the second are

`3x-4=2x-1=>x=3` and `y=2*3-1=5`

Answer 2

`x = 3`
`y = 5`

Explanation:

`y= 3x - 4` `rArr` 1st equation
`2x - y = 1` `rArr` 2nd equation

Since `y` is already the subject of the first equation, all you need to do is substitute `y = 3x - 4` into the 2nd equation!

So,

`2x - (3x - 4) = 1`

Expand the brackets.

`2x - 3x + 4 = 1`

Which gets you:

`-x + 4 = 1`

Move the 4 over so `x` becomes your subject.

`-x = -4 + 1`
`-x = -3`

Switch them over so your `x` is positive!

`3 = x`

To find `y`, just substitute `x = 3` into either the 1st of 2nd equation.

So,

`y = 3(3) - 4`
`y= 9 - 4`
`y = 5`

To check:
Substitute the values of `x` and `y` back into the equation. You will get the same answer.