Is 0x + 6y = 3 is linear equation in two variables?
The Correct Answer and Explanation is:
Yes, the equation 0x+6y=30x + 6y = 30x+6y=3 is a linear equation in two variables.
A linear equation in two variables generally follows the form:Ax+By=CAx + By = CAx+By=C
where AAA, BBB, and CCC are constants, and xxx and yyy are the variables. In this case, the equation can be rewritten as:0x+6y=30x + 6y = 30x+6y=3
Here, A=0A = 0A=0, B=6B = 6B=6, and C=3C = 3C=3. The term involving xxx is absent (which is why it’s 0x0x0x). This does not affect the linearity of the equation because the definition of a linear equation in two variables only requires that the variables xxx and yyy appear to the first power, and the coefficients of the variables are constants.
To verify whether this equation is linear, we can rewrite it as:6y=36y = 36y=3
By dividing both sides by 6, we get:y=12y = \frac{1}{2}y=21
This is an equation where yyy is equal to a constant (12\frac{1}{2}21). This describes a horizontal line at y=12y = \frac{1}{2}y=21 in the xyxyxy-plane. Since a horizontal line is indeed a straight line, this equation represents a linear relationship.
Thus, even though the xxx-variable doesn’t explicitly appear, the equation remains linear because the degree of the variables is 1 and the equation represents a straight line in the coordinate plane. Therefore, 0x+6y=30x + 6y = 30x+6y=3 is a valid linear equation in two variables.
