Question

SW=2x+y, WC= x-2y, W is the midpoint of SC, and SC=20, find the values of x and y.

Answer 1

`x= 6`

`y = -2`

Explanation:

Given

`SW = 2x + y`

`WC = x - 2y`

`SC = 20`

Required

Determine x and y

Since W is the midpoint;

`SW = WC = (1)/(2) * SC`

`SW = WC = (1)/(2) * 20`

`SW = WC = 10`

Substitute 10 for SW and WC

`2x + y = 10` --- (1)

`x - 2y = 10` ---- (2)

Make x the subject in (2)

`x = 10 + 2y`

Substitute
`x = 10 + 2y` in (1)

`2(10 + 2y) + y = 10`

`20 + 4y + y = 10`

`20 + 5y = 10`

Solve for 5y

`5y = 10 - 20`

`5y = -10`

Solve for y

`y = -10/5`

`y = -2`

Recall that
`x = 10 + 2y`

`x = 10 + 2(-2)`

`x = 10 -4`

`x= 6`