An important and conceptual question from linear equations in two variables in which we have to find the number of solutions of given equations x+2y-8=0, 2x+4y=16

Kindly solve the above equations

RS Aggarwal, Class 10, chapter 3F, question no 1

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## x+2y=8

And 2x+4y=16

These given equations are in the form:

a1x+b1y+c1=0 and

a2x+b2y+c2=0

Where

a1=1,b1=2 and c1=8

a2=2,b2=4 and c2=16

a1/a2=1/2, b1/b2=2/4=1/2

As we know, the condition for the equations to have infinitely many solutions is

a1/a2=b1/b2=c1/c2

So, system has infinitely many solutions