Give the complete real solution set of the two linear equations.

01 / Standard#Your turn

x+y+z=2,\quad3x+y-z=4

Official paper · jm02-2026 · 5(b)(i) · PDF 7

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Subtract the first equation from the second.

Hint 2

Choose z as the free real parameter.

Worked solution

Elimination gives the relation between x and z.
$2x-2z=2\implies x=z+1$
Set z=t and recover y from the first equation.
$(x,y,z)=(1+t,1-2t,t),\quad t\in\mathbb R$

(x,y,z)=(1+t,1−2t,t), t∈ℝ.

Checks and common pitfalls: Two independent equations in three unknowns leave one free parameter.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Elimination gives the relation between x and z.
$2x-2z=2\implies x=z+1$
Set z=t and recover y from the first equation.
$(x,y,z)=(1+t,1-2t,t),\quad t\in\mathbb R$

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

2026 JM02