Is 4x^2-2y=-4 a linear equation in two variables

Question

asked Jan 19, 2024 159k views

1 Answer

Mark Schill · Answer 1 · 2024-01-23T22:55:46+0000

$\large\bf{\underline{\underline{\mathfrak{Question}:}}}$

Is 4x^2-2y=-4 a linear equation in two variables?

$\large\bf{\underline{\underline{\mathfrak{Solution}:}}}$

Given that,

${\small{\rm{4x^2-2y=-4}}}$

Here, the given equation is not an example of linear equation in two variables.

This equation can also be written as,

${\small{\rm{4x^2-2y+4=0}}}$

Here the degree of the polynomial is 2 and also it is not written in the general form of linear equation in two variable.

Note that, the degree of the linear polynomial must be one.

The general form of a linear equation in two variable is,

${\boxed{\small{\rm{ax+by=c\:or\:ax+by+c=0}}}}$

Here,

$:{\Longrightarrow{\small{\rm{a,b\:and\:c\:are\:real\:numbers.}}}}$

In addition,

${:\Longrightarrow{\small{\rm{a\:or\:a^2\cancel=\:0\:and\:b\:or\:b^2\cancel=\:0}}}}$

A linear equation has at least one solution, no solution, unique solution or an Infinitely many solutions.