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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 \(p, r, q\)

-3p - r - 3q = -14

p - r + q = -2

-3p - r + q = -14

The equations are numbered in the order shown

(a)1 mark

Which approach begins by producing two equations in \(p\) and \(q\)?

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

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

(b)1 mark

Choose the reduced system that removes \(r\) and preserves the displayed equations

R_1': 4q = 0\qquad R_2': 4p = 12

R_1': -4q = 0\qquad R_2': 4p = 12

R_1': -4q = 0\qquad R_2': -\frac{4}{3}r + \frac{4}{3}q = -\frac{20}{3}

Give the exact solution for the system

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