Conditions for a system of linear equations to have infinite solutions
The number of...
Question
The number of integral solution to the system of equation a1+a2+a3+a4+a5=25 and a1+a2+a3=10 are
A
28+25
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B
210+25
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C
225+210
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D
Infinite
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Solution
The correct option is D Infinite We have, a1+a2+a3+a4+a5=25..........(1) and a1+a2+a3=10 .........(2) By, (2)−(1) a4+a5=15 ....(3) Let a4=x,a5=y ⇒x+y=15.......(4)
Here x and y are integers. So number of integral solution will be infinite, since we have one equation and two unknowns