Question

Which of the following linear equations does not pass through the origin?

• A. $3x+4y=0$
• B. $5x=9y$
• C. $2x+1=y$
• D. $x=8y$

Answer 1

The correct option is C $2x+1=y$

A linear equation in two variables passes through the origin (0, 0), if it satisfies the point (0, 0).
Consider the equations:
$3x+4y=0$ …..(i)
$5x=9y$ …..(ii)
$2x+1=y$ …..(iii)
$x=8y$ …..(iv)
Substituting x = 0 and y = 0 in (i), we get
$3\left(0\right)+4\left(0\right)=0$
$\Rightarrow 0=0$ (True)
Substituting x = 0 and y = 0 in (ii), we get
$5\left(0\right)=9\left(0\right)$
$\Rightarrow 0=0$ (True)
Substituting x = 0 and y = 0 in (iii), we get
$2\left(0\right)+1=0$
$\Rightarrow 1=0$ (False)
Substituting x = 0 and y = 0 in (iv), we get
$0=8\left(0\right)$
$\Rightarrow 0=0$ (True)
Therefore, the linear equation $2x+1=y$ does not pass through the origin.
Hence, the correct answer is option (c).