Question

What is the solution to the following system?

a(2, 3, 4)
b(4, 3, –2)
c(4, 3, 2)
d(6, 7, –2)

Answer 1

C

Explanation:

Answer 2

The answer is x = 4, y = 3, z = 2.
Solution:
We solve this given system of equations using elimination. We choose to eliminate variable z first by taking the sum of the first and second equations:
3x + 2y + z = 20 (equation 1)
x - 4y - z = -10 (equation 2)
(equation 1) + (equation 1) => 4x - 2y = 10 (equation 4)

We now select the second and third equations and eliminate the same variable z:
x - 4y - z = -10 (equation 2)
2x + y + 2z = 15 (equation 3)
(equation2 multiply by 2) + (equation 3) => 2x - 8y - 2z = -20
2x + y + 2z = 15
=> 4x - 7y = -5 (equation 5)

We solve for y by subtracting the fifth equation from the fourth:
(equation 4) + (equation 5) => 5y = 15
y = 3

We substitute y = 3 into the fourth equation to find x.
4x - 2y = 10
4x - 2(3) = 10
4x = 16
x = 4

We use y = 3 and x = 4 and substitute into the first equation to solve for z.
3x + 2y + z = 20
3(4) + 2(3) + z = 20
12 + 6 + z = 20
z = 2
Therefore, the solution is x = 4, y = 3, z = 2.