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Question

Find those values of m the system of equation
2x+my4=0
3x7y10=0
for which (1) there is unique solution
and (2) there is no solution.

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Solution

Given equations are
2x+my4=0
3x7y10=10
Here a1=2,b1=m,c1=4,a2=3,b2=7,c2=10
(i) When equations have a unique solution, then
a1a2b1b2
23m7
m143
(ii) When the equation have no solution, then
a1a2=b1b2c1c2
23=m7410
23=m7 (from first two terms)
m=143

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