Answer:
x = 6
y = 3
z = 6
Explanation:
substitute z = 2y into x + y + z = 15. this gives x + y + 2y = x+ 3y = 15. From this, express x in terms of y: x = 15 - 3y.
now, substitute x = 15 - 3y and z = 2y into 6x + 5y + 2z = 63.
this gives
6x + 5y + 2z = 6(15 - 3y) + 5y + 2(2y)
= 90 - 18y + 5y + 4y
= 90 - 9y.
we know this is equal to 63:
90 - 9y = 63
thus
9y = 90 - 63 = 27
and
y = 3.
use the fact that y = 3 to determine the values of x and z:
x = 15 - 3y = 15 - 3*3 = 6.
z = 2y = 2*3 = 6.