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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 \(c, a, b\)

3c + 2a + b = 29

-3c - 3a - 2b = -33

3c - a - b = 20

The equations are numbered in the order shown

(a)1 mark

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

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

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

(b)1 mark

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

R_1': -9c - b = 69\qquad R_2': -12c + b = -93

R_1': 9c - b = 69\qquad R_2': -12c + b = -93

R_1': 6c + a = 49\qquad R_2': -9c - a = -73

Enter the exact value of each variable

\(c\) \(a\) \(b\)