Questions: What is a linear equation? ∛(x)-3=y 2x-4y-6=0 -√x y=12 2x=y^2

Solution Steps

To determine whether each equation is a linear equation, we need to check if the equation can be written in the form \( ax + by + c = 0 \), where \( a \), \( b \), and \( c \) are constants, and \( x \) and \( y \) are variables. A linear equation should not have variables raised to any power other than 1, nor should it involve roots or products of variables.

The first equation is \( \sqrt[3]{(x)} - 3 = y \). This equation contains a cube root of \( x \), which is a non-linear term. Therefore, it is not a linear equation.

The second equation is \( 2x - 4y - 6 = 0 \). This equation can be rearranged to the standard form \( ax + by + c = 0 \) with \( a = 2 \), \( b = -4 \), and \( c = -6 \). Since it contains only linear terms, it is a linear equation.

The third equation is \( -\sqrt{x}y = 12 \). This equation includes a square root of \( x \), which makes it non-linear. Thus, it is not a linear equation.

The fourth equation is \( 2x = y^2 \). This equation contains \( y^2 \), which is a quadratic term, indicating that it is also non-linear.

Final Answer