3x+2y=5 and 6x+4y=10 ifa1/a2 than these simultaneous equations have

1.	3x+2y=5 and 6x+4y=10 ifa1/a2 than these simultaneous equations have
Answer» $\huge\boxed{\underline{\underline{\green{Solution}}}}$ $\displaystyle \: \longmapsto \: \:$ FORMULA TO BE IMPLEMENTED A PAIR of Straight Lines $\displaystyle \: a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0$ have infinite NUMBER of solutions if $\displaystyle \: \: \frac{a_1}{a_2} = \frac{b_1}{b_2}=\frac{c_1}{c_2}$ $\displaystyle \: \longmapsto \: \:$ CALCULATION : GIVEN pair of linear EQUATIONS $3x +2y = 5 \: \: and \: \: 6x + 4y =10$ Comparing with $\displaystyle \: a_1x+b_1y+c_1=0 \: and \: \: a_2x+b_2y+c_2=0$ We get $\displaystyle \: a_1 = 3 \: , \: b_1 = 2 \: , c_1= 5 \: and \: \: a_2 = 6 \: , \: b_2 = 4\: , \: \: c_2= 10$ $\displaystyle \: \frac{a_1}{a_2} = \frac{3}{6} = \frac{1}{2}$ $\displaystyle \: \frac{b_1}{b_2} = \frac{2}{4} = \frac{1}{2}$ $\displaystyle \: \frac{c_1}{c_2} = \frac{5}{10} = \frac{1}{2}$ So $\displaystyle \: \: \frac{a_1}{a_2} = \frac{b_1}{b_2}=\frac{c_1}{c_2}$ Hence given SYSTEM of equations have infinite number of solutions

Answer»

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