Question

What is the solution to the system of equations ?

x+y+z=15
z=2y
6x+5y+2z=63

Answer 1

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.