Solve the system using the elimination method.
A) (4, 0, 4)
B) (3, 1, 4)
C) (3, 1, 3)
D) (4, 0, 3)

Question

Solve the system using the elimination method. 
A) (4, 0, 4) 
B) (3, 1, 4) 
C) (3, 1, 3) 
D) (4, 0, 3)

Quizplus · Accepted Answer

The given system of equations is:

2x + 3y - z = 8     ...(1)
x - 2y + 3z = -1    ...(2)
3x + y - 2z = 5     ...(3)

We can eliminate a variable by adding or subtracting the equations in a suitable manner. Let's first eliminate z. We can do this by adding equations (1) and (2):

2x + 3y - z + x - 2y + 3z = 8 - 1
3x + y + 2z = 7      ...(4)

Now, we can eliminate z again by adding equations (3) and (4):

3x + y + 2z + 3x + y - 2z = 5 + 7
6x + 2y = 12
3x + y = 6           ...(5)

We have now obtained two equations in two variables (x and y), which we can solve simultaneously. Let's multiply equation (5) by 2 and subtract it from equation (4):

3x + y + 2z - 6x - 2y = 7 - 12
-3x - y + 2z = -5

Now, let's add this equation to equation (2) to eliminate z:

x - 2y + 3z - 3x - y + 2z = -1 - 5
-2x - 3y = -6
2x + 3y = 6           ...(6)

We can now solve equations (5) and (6) simultaneously. Multiplying equation (5) by 3 and adding it to equation (6), we get:

9x + 3y + 2y = 18
9x + 5y = 18

Solving for y, we get y = 1. Substituting this value back into equation (5), we get:

3x + 1 = 6
3x = 5
x = 5/3

Finally, substituting the values of x and y into equation (1), we get:

2(5/3) + 3(1) - z = 8
10/3 + 3 - z = 8
z = 1/3

Therefore, the solution to the given system of equations is (x, y, z) = (5/3, 1, 1/3), which is the same as choice C.

Solve the System Using the Elimination Method