Question

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

Answer 1

Using substitution, you can find the solution is `x=1, y=3`

Explanation:

The second expression `y=2x+1` is already an expression ready to substitute! Since we know what `y` is equivalent to, we can substitute it into the first expression:

`x+y=4`

`x+(2x+1)=4 rArr x+2x+1=4`

`x(1+2)+1=4 rArr 3x+1=4`

`3xcancel(+1-1)=4-1 rArr 3x=3`

`color(red)(x=1)`

Now that we know what `x` is equivalent to, we can solve for `y`

`y=2x+1 rArr y=2(1)+1=2+1`

`color(blue)(y=3)`