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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 \(r, p, q\)

2r + 2p + q = 12

-r + 3p + q = -12

-r - 2p + 2q = -16

The equations are numbered in the order shown

(a)1 mark

Choose the first step that directly gives a two-equation system in \(r\) and \(p\)

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

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

(b)1 mark

Which pair or set of equations has \(q\) removed correctly?

R_1': 3r - p = 24\qquad R_2': r - 8p = 8

R_1': -3r - p = 24\qquad R_2': r - 8p = 8

R_1': \frac{8}{3}r + \frac{1}{3}q = 20\qquad R_2': -\frac{5}{3}r + \frac{8}{3}q = -24

Determine the solution vector, keeping the variable labels in place

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