Question

How many solutions did a linear equation 2x + 4y = 0 have ?

Answer 1

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$\longmapsto \: \:$ PROCEDURE

A general equation of any linear equation is

$\displaystyle \: \: \: \: ax + by + c = 0$

This also the general equation of any line

If c = 0 then

$\displaystyle \: \: \: \: ax + by + c = 0 \: \: converted \: \: to \: \: \displaystyle \: \: \: ax + by = 0$

Which is the equation of a line passing through origin

Any point on the line

$\displaystyle \: \: \: \: ax + by = 0 \: \: is \: \: a \: \: solution \: \: of \: \: \displaystyle \:\: ax + by= 0$

$\longmapsto$CALCULATION

The given equation of the linear equation is

$\displaystyle \: \: \: \: 2x + 4y = 0$

Hence any point on the line

$\displaystyle \: \: \: \: x + 2y = 0$

is a solution of the given linear equation

There are infinite number of solutions of the given linear equation

For example ( 2, - 1 ), ( 4,-2) are the solutions of the given linear equation