Question

How do you solve `x = 4y` and `2x + 3y = 44` using substitution?

Answer 1

You have `x = 4y`, so, what you do is, substitute `4y` wherever you see `x` in the second equation. This sequence looks like:

`2x + 3y = 44`

`2(4y) + 3y = 44`

`8y + 3y = 44`

`11y = 44`

`y = 44/11 = 4`

...now that you know that y = 4, you can plug this in to either equation and solve for x.

`x = 4y = 4(4)`

`x = 16`

CHECK YOUR WORK. Feed these values into each equation to verify that they are actually solutions.

`x = 4y`
`16 = 4 * 4` CHECK

`2x + 3y = 44`

`(2 * 16 ) + (3 * 4) = 32 + 12 = 44` CHECK

GOOD LUCK

Answer 2

`(x,y)to(16,4)`

Explanation:

`x=4yto(1)`

`2x+3y=44to(2)`

`color(blue)"substitute "x=4y" into equation "(2)`

`2(4y)+3y=44`

`8y+3y=44`

`11y=44rArry=44/11=4`

`"substitute "y=4" into equation "(1)`

`x=4xx4=16`

`"point of intersection "=(16,4)`