Question

How do you solve `5x + 8y = 7` and `x + y = 2` using substitution?

Answer 1

x=3, y= -1

Explanation:

given x+y=2
y= 2 - x (eq. 1)

given 5x+8y=7 (eq.2)

substitute eq. 1 in eq. 2

5x + 8(2-x) =7
5x + 16 - 8x = 7 (open the bracket)
-3x=7-16= -9
x= -9/ -3 = 3

eq 1-
y= 2-3= -1

so x=3, y= -1

Answer 2

`(x,y)=(3,-1)`
See below for method of solution by substitution.

Explanation:

If `x+y=2`
then `y=2-x`
and
`color(white)("XXX")(2-x)` can be substituted for `y` in `5x+8y=7`

This would give:
`color(white)("XXX")5x+8(2-x)=7`

`color(white)("XXX")5x+16-8x=7`

`color(white)("XXX")-3x=-9`

`color(white)("XXX")x= 3`

Then, returning to `y=2-x`
we have
`color(white)("XXX")y=2-3 =-1`