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Solve a linear system with three or four unknowns

Question 1 of 8

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Consider the three-equation linear system in the variables \(p, q, r\)

2p + q + r = 20

-p + 3q + 3r = 4

3p + 2q - 3r = 12

The equations are numbered in the order shown

(a)1 mark

Which method directly produces two equations in \(q\) and \(r\)?

Eliminate a different variable in each pair before solving the reduced equations

Use the equation with a coefficient of -1 for \(p\) to substitute into the other equations

(b)1 mark

Select the valid reduced equations after removing \(p\)

R_1': -7q + 7r = 28\qquad R_2': 11q + 6r = 24

R_1': \frac{7}{3}p = \frac{56}{3}\qquad R_2': 2p + 5q = 16

R_1': 7q + 7r = 28\qquad R_2': 11q + 6r = 24

Find all variable values in the order labelled below

\(p\) \(q\) \(r\)