Question

Solve the following as per the given instructions.
(i) Write any three linear equations in two variables using the variables x and y.
(ii) Is 7x² + 4y³ = 17 a linear equation in two variables ? Justify.
(iii) $5x+\sqrt{p}y=10$ is a linear equation in two variables x and y. What is the condition for the value of p?
(iv) Write the solutions of the equation x + y = 18. Write your observation.
(v) If x = 1, y = a is the solution of the equation x + 3y = 100, then find a.

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\mathrm{Three}\mathrm{linear}\mathrm{equations}\mathrm{in}\mathrm{two}\mathrm{variables}\mathrm{are}: \\ x+y=8,5x-6y=2,2x+3y=4 \\ \left(\mathrm{ii}\right)\mathrm{No},\mathrm{a}\mathrm{linear}\mathrm{equation}\mathrm{in}\mathrm{two}\mathrm{variable}x\mathrm{and}y\mathrm{is}\mathrm{of}\mathrm{the}\mathrm{form}ax+by=c,\mathrm{where} \\ a,b\text{and}c\mathrm{are}\mathrm{real}\mathrm{numbers}. \\ \left(\mathrm{iii}\right)\mathrm{p}\mathrm{is}\mathrm{a}\mathrm{real}\mathrm{number}\mathrm{and}p>0. \\ \left(\mathrm{iv}\right)\mathrm{There}\mathrm{can}\mathrm{be}\mathrm{infinite}\mathrm{solutions}\mathrm{to}\mathrm{this}\mathrm{equation} \\ \mathrm{One}\mathrm{of}\mathrm{the}\mathrm{solution}s: \\ \text{W}\mathrm{hen}x=0 \\ \Rightarrow 0+y=18 \\ \Rightarrow y=18 \\ (0,18)\mathrm{is}\mathrm{the}\mathrm{solution}. \\ \left(\mathrm{v}\right)x+3y=10 \\ \mathrm{Substituting}x=1\mathrm{and}y=a,\text{we get}: \\ 1+3a=10 \\ \Rightarrow 3a=9 \\ \Rightarrow a=3 \end{gathered}$$