Question

2
.
The pair of equations x+2y+5 = 0 and -3x-6y+1 = 0 have
a) unique solution
b) exactly two solutions
c) infinitely many solutions
d) no solution​

Answer 1

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$\setlength{\unitlength}{1.6mm}\begin{picture}(30,20)\linethickness{0.1mm}\multiput(0,0)(0.5,0){2}{\line(0,-1){47}}\footnotesize{\put(2,-2){Now Applying This fact to the above problem}}\footnotesize{\put(8,-5){x+2y+5 = 0}}\footnotesize{\put(7,-7){-3x-6y+1 = 0}}\footnotesize{\put(2,-10){ \therefore\:a_1=1\:\:\:\:\:b_1=2\:\:\:\:\:c_1=5 }}\footnotesize{\put(2,-12){ \therefore\:a_2=-3\:\:b_2=-6\:\:c_2=1 }}\footnotesize{\put(2,-17){ \dfrac{a_1}{a_2}=\dfrac{1}{-3} }}\footnotesize{\put(2,-22){ \dfrac{b_1}{b_2}=\dfrac{2}{-6}=\dfrac{1}{-3} }}\footnotesize{\put(2,-27){ \dfrac{c_1}{c_2}=\dfrac{2}{-6}\neq\dfrac{5}{1} }}\footnotesize{\put(2,-32){ \therefore\:\:\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2} ( will have no solution)}}\footnotesize{\put(2,-37){ \blacksquare \underline{\:AnsweR}}}\footnotesize{\put(2,-37){ \blacksquare \underline{\:AnsweR}}}\footnotesize{\put(2,-40){option (d) no solutions.. }}\put(2,-46){\line(1,0){40}}\end{picture}$