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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 \(u, w, v\)

u + w + 2v = 17

-3u + w - v = -21

-u + 2w + v = 1

The equations are numbered in the order shown

(a)1 mark

Which first plan directly produces a two-equation system in \(u\) and \(w\)?

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

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

(b)1 mark

Which reduced system results after removing \(v\)?

R_1': -5u + 3w = -25\qquad R_2': -4u + 3w = -20

R_1': 4u + 3v = 38\qquad R_2': 5u + 3v = 43

R_1': 5u + 3w = -25\qquad R_2': -4u + 3w = -20

Enter the exact value of each variable

\(u\) \(w\) \(v\)