Question

Which of the following equations are linear equation in two variables?

• A. $y=x^2+3x$
• B. $7y=3x-10$
• C. $\frac{x}{y}=\frac{5}{3}$
• D. $\frac{5x+6x^2}{x}=y$

Answer 1

Answer: (B), (C), (D)

$\frac{5x+6x^2}{x}=y$

For a equation to be linear in two variable, exponent of both variable should be $1$ i.e. and that equation will represent straight line.
$\underset{–}{option\left(a\right)}:$ $y=x^2+3x$.
This is not linear because $x$ is having exponent $2$.
$\underset{–}{option\left(b\right)}:$ $7y=3x-10$.
This is linear because $x$ and $y$ is having exponent $1$.
$\underset{–}{option\left(c\right)}:$ $\frac{x}{y}=\frac{5}{3}$
This is linear because $x$ and $y$ is having exponent $1$.
$\underset{–}{option\left(d\right)}:$$\frac{5x+6x^2}{x}=y$
On simplifying by taking $x$ comman from numerator we get,
$\frac{x(5+6x)}{x}=y$.
$\Rightarrow 5+6x=y$
So, This is linear because $x$ and $y$ is having exponent $1$.