Question

How do you solve `2x + y = 5` and `y = 3x + 2` using substitution?

Answer 1

`x=3/5`
`y=19/5`

Explanation:

`2x+y=5`
Putting `y=3x+2` in the above equation we get
`2x+3x+2=5`
or
`5x+2=5`
or
`5x=5-2`
or
`5x=3`
or
`x=3/5`=======Ans `1`
By putting `x=3/5` in the equation `y=3x+2`
we get
`y=3(3/5)+2`
or
`y=9/5+2`
or
`y=(9+2(5))/5`
or
`y=(9+10)/5`
or
`y=19/5`=====Ans `2`

Answer 2

`x = 3/5, y = 3 4/5`

Explanation:

This type of question is particularly common when working with straight lines.

Note that there is a single `y` term in both equations.

`y = -2x+5" and " y = 3x +2`

At the point where the two lines intersect, the `x- and y-` values are equal.

If `" y = y" "` it follows that:

`3x +2 =-2x+5`

`5x = 3`

`x = 3/5`

There are now two equations to find a value for y. If we get the same answer for each we will know our answers are correct.

`y = 3xx 3/5 +2 = 3 4/5" "y = -2 xx3/5 +5 = 3 4/5`