Question

9.

Solve the following system of equations
3x −2y + 4z = 20
−x + 5x +12z = 73
x + 3y −2z = 1

Select the appropriate response:

A) x =4, y = 3, z = 5
B) x = 2, y = 3, z = 5
C) x = 5, y = 5, z = 5
D) x = 7, y =8, z = 5

Answer 1

B) x = 2, y = 3, z = 5

Explanation:

3x −2y + 4z = 20

3(2) - 2(3) + 4(5) = 20

20 = 20

−x + 5y +12z = 73

-2 + 5(3) + 12(5) = 73

73 = 73

x + 3y −2z = 1

2 + 3(3) - 2(5) = 1

1 = 1

Answer 2

B) x = 2, y = 3 and z = 5.

Explanation:

3x −2y + 4z = 20 .....A

-x + 5y+ 12z = 73 .....B

x + 3y −2z = 1 ......C

Adding B and C:

8y + 10z = 74 .... E

Multiply equation B by -3:

-3x - 9y + 6z = -3

Add this equation to A:

-11y + 10z = 17

Subtract this equation fro E:

19y = 57

y = 3.

Substitute y = 3 in equation E:

8*3 + 10z = 74

10z = 50

z = 5.

Finally substitute y = 3 and z = 5 into equation C:

x + 3(3) - 2(5) = 1

x + 9 - 10 = 1

x = 1 + 1

x = 2.