Question

Select the correct answer. What is the solution of this linear system? { p+ q +r=32, p-r=4, 2p+q=36 A. (16,8,8) B. C. D. E.

Answer 1

To solve the given linear system, we can use the method of substitution or elimination. Here, I will use elimination. The solution to the linear system is (p, q, r) = (15.2, 5.6, 11.2).

Step-by-step explanation:

To solve the given linear system, we can use the method of substitution or elimination. Here, I will use elimination:

Step 1: Add the first and third equation to eliminate q:
p + q + r = 32
2p + q = 36
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3p + r = 68

Step 2: Multiply the second equation by 2 to eliminate q:
2(p - r) = 8
2p - 2r = 8

Step 3: Add the equations obtained in steps 1 and 2 to eliminate r:
3p + r = 68
2p - 2r = 8
------------------
5p = 76

Step 4: Solve for p:
p = 76/5 = 15.2

Step 5: Substitute the value of p back into one of the original equations to solve for q:
2(15.2) + q = 36
30.4 + q = 36
q = 36 - 30.4 = 5.6

Step 6: Substitute the values of p and q back into one of the original equations to solve for r:
p + q + r = 32
15.2 + 5.6 + r = 32
r = 32 - 20.8 = 11.2

Therefore, the solution to the given linear system is (p, q, r) = (15.2, 5.6, 11.2).