Question

Given the linear equation 3x+4y=9 write another linear equation in these two variable such that the geometrical representative of the pair so formed is
a) intersecting line
b) coincident line

Answer 1

Dear student
$$\begin{gathered} \left(\mathrm{a}\right)4\mathrm{x}+3\mathrm{y}=1 \\ \mathrm{As}\frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}\ne \frac{{\mathrm{b}}_1}{{\mathrm{b}}_2}\mathrm{in}\mathrm{this}\mathrm{case} \\ \mathrm{where}{\mathrm{a}}_1=3,{\mathrm{b}}_1=4 \\ \mathrm{and}{\mathrm{a}}_2=4\mathrm{and}{\mathrm{b}}_2=3 \\ \left(\mathrm{b}\right)6\mathrm{x}+8\mathrm{y}=18 \\ \mathrm{As}\frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}=\frac{{\mathrm{b}}_1}{{\mathrm{b}}_2}=\frac{{\mathrm{c}}_1}{{\mathrm{c}}_2}\mathrm{in}\mathrm{this}\mathrm{case} \\ \mathrm{where}{\mathrm{a}}_1=3,{\mathrm{b}}_1=4,{\mathrm{c}}_1=-9 \\ \mathrm{and}{\mathrm{a}}_2=6\mathrm{and}{\mathrm{b}}_2=8\mathrm{and}{\mathrm{c}}_2=-18 \end{gathered}$$

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