Question

# $9x+3y+12=0\phantom{\rule{0ex}{0ex}}18x+6y+24=0$

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Solution

## Step 1: Compare both given equations $9x+3y+12=0\phantom{\rule{0ex}{0ex}}18x+6y+24=0$with the general form of pair of linear equations ${a}_{1}x+{b}_{1}y+{c}_{1}=0\phantom{\rule{0ex}{0ex}}{a}_{2}x+{b}_{2}y+{c}_{2}=0$in two variables On comparing,${a}_{1}=9,{b}_{1}=3,{c}_{1}=12\phantom{\rule{0ex}{0ex}}{a}_{2}=18,{b}_{2}=6,{c}_{2}=24$Step 2: Compare the ratios of $\frac{{a}_{1}}{{a}_{2}},\frac{{b}_{1}}{{b}_{2}},and\frac{{c}_{1}}{{c}_{2}}$$\frac{{a}_{1}}{{a}_{2}}=\frac{9}{18}=\frac{1}{2}$$\frac{{b}_{1}}{{b}_{2}}=\frac{3}{6}=\frac{1}{2}$$\frac{{c}_{1}}{{c}_{2}}=\frac{12}{24}=\frac{1}{2}$On Comparing, $\frac{{a}_{1}}{{a}_{2}}=\frac{{b}_{1}}{{b}_{2}}=\frac{{c}_{1}}{{c}_{2}}$$=\frac{1}{2}$ ( If $\frac{{a}_{1}}{{a}_{2}}=\frac{{b}_{1}}{{b}_{2}}=\frac{{c}_{1}}{{c}_{2}}$ then the pair of equation has $Infinitelymanysolution$)Hence, the given equation $9x+3y+12=0\phantom{\rule{0ex}{0ex}}18x+6y+24=0$ has $Infinitelymanysolution$

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