Question

How do you solve the system `x = y + 4` and `2x - 5y = 2` by substitution?

Answer 1

`x = y + 4` -----------(1)
`2x - 5y = 2`-----------(2)

Substituting `x` from the first equation into the second one gives us:

`2(y+4) - 5y = 2`

`2y+8 - 5y = 2`

`-3y + 8 = 2`

`-3y = 2-8`

`-3y = -6`

Dividing both sides by `-3` will give us:

`(cancel(-3)y)/cancel(-3) = (-6)/-3`

`color(green)(y = 2`

Substituting `y=2` in the first equation will give us :

`x = 2 + 4`

`color(green)(x = 6`

The solution to both these equations :`x = 6; y = 2`

Verify :

Substitute the values of `x and y` in both the equations to see if they are satisfied