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

Answer:

$x= 6$

$y = -2$

Step-by-step explanation:

Given

$SW = 2x + y$

$WC = x - 2y$

$SC = 20$

Required

Determine x and y

Since W is the midpoint;

$SW = WC = \frac{1}{2} * SC$

$SW = WC = \frac{1}{2} * 20$

$SW = WC = 10$

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 $x = 10 + 2y$

$x = 10 + 2(-2)$

$x = 10 -4$

$x= 6$