Question

How do you solve `5x + 2y = 20` and `x + 4y = 13`?

Answer 1

`(x,y)to(3,5/2)`

Explanation:

`5x+2y=20to(1)`

`x+4y=13to(2)`

`"from equation "(2)" we can express x in terms of y"`

`rArrx=13-4yto(3)`

`"substitute "x=13-4y" in equation "(1)`

`5(13-4y)+2y=20larrcolor(blue)"distribute"`

`rArr65-20y+2y=20`

`rArr-18y+65=20larrcolor(blue)"subtract 65 from both sides"`

`rArr-18y=-45`

`"divide both sides by "-18`

`(cancel(-18) y)/cancel(-18)=(-45)/(-18)`

`rArry=45/18=5/2`

`"substitute "y=5/2" in equation "(3)`

`rArrx=13-(4xx5/2)=13-10=3`

`"the solution is "(x,y)to(3,5/2)`

Answer 2

x=3, y=5/2

Explanation:

(1) `5x+2y=20`
(2) `x+4y=13`

First, multiply equation 1 by 2, this gives both equations the same y coefficient of 4. The equations are now:
(1) `10x+4y=40`
(2) `x+4y=13`

Next subtract equation 2 from 1 (equation 1 - equation 2)
This makes
`(10x-x) + (4y-4y) = (40-13)`

Simplified: `9x-0=27`

Then divide both sides by 9 to solve for x

`9/9x=27/9`
`x=3`

Then input x=3 back into equation 2

`(3)+4y=13`

Subtract 3 from both sides:
`4y=10`

Divide both sides by 4 to solve for y

`y=10/4` (simplified to `5/2`)

Therefore `x=3` and `y=5/2`