IGNOU MTE 4 2026 - Using the method of substitution, obtain the solution set in , of

Question

Using the method of substitution, obtain the solution set in $\mathbb{R}^3$ , of the following:

i) $x - \pi = 5$

ii) $2x - y + z = 1, x - 2y + z = 3, y = \sqrt{2} - z$

iii) $x - y = 5, x = 7, 2x - 3y = 5$

09 Jan 2026

Answer :

Word Count : 248

In ℝ³, for the equation x − π = 5, solving by substitution gives x = 5 + π. Since there are no restrictions on y and z, the solution set is {(5 + π, y, z) : y, z ∈ ℝ}. For the system 2x − y + z

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