Question

the pair of linear equations represents wat type of solutions? x-2y=5 , 2x-4y=10

Answer 1

$$\begin{gathered} x-2y=5----\left(1\right) \\ 2x-4y=10 \\ \Rightarrow x-2y=5-----\left(2\right) \\ \mathrm{Now},\mathrm{here}{a}_1=1,a_2=1,b_1=-2,b_2=-2,c_1=5,c_2=5 \\ \mathrm{We}\mathrm{can}\mathrm{see}\mathrm{that} \\ \frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}=\frac{1}{1}, \\ \frac{{\mathrm{b}}_1}{\mathrm{b}2}=\frac{-2}{-2}=\frac{1}{1}, \\ \frac{{\mathrm{c}}_1}{{\mathrm{c}}_2}=\frac{5}{5}=\frac{1}{1} \\ \mathrm{We}\mathrm{can}\mathrm{see}\frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}=\frac{{\mathrm{b}}_1}{\mathrm{b}2}=\frac{{\mathrm{c}}_1}{{\mathrm{c}}_2}. \\ \mathrm{Lines}\mathrm{are}\mathrm{coincident}\mathrm{and}\mathrm{have}\mathrm{infinitely}\mathrm{many}\mathrm{solutions}. \end{gathered}$$