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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 \(y, z, x\)

3y + z - x = -11

y - z - x = 3

y - x = -2

The equations are numbered in the order shown

(a)1 mark

Which method directly produces two equations in \(y\) and \(z\)?

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

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

(b)1 mark

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

R_1': z + 2x = -5\qquad R_2': -z = 5

R_1': -2y + z = -9\qquad R_2': -z = 5

R_1': 2y + z = -9\qquad R_2': -z = 5

Find all variable values in the order labelled below

\(y\) \(z\) \(x\)