Find the general solution when k=3.

01 / Standard#Your turn

\begin{cases}x+y+z=1\\kx+5y+z=3\\x+ky-z=1\end{cases}

Official paper · jm02-2024 · 5(b)(ii) · PDF 7

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Eliminate x using the first two equations.

Hint 2

Use a free parameter and check the third equation.

Worked solution

(x,y,z)=(1−2t,t,t), t∈ℝ.

Checks and common pitfalls: The third equation is dependent, so t remains free.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Subtract three times equation 1 from equation 2.
$2y-2z=0\implies y=z=t$
Recover x and verify the third relation.
$x=1-2t,\quad x+3y-z=1-2t+3t-t=1$

Think first. Reveal a hint when the class is ready.

2024 JM02