Question

Determine whether the following equations are linear in x, y and z; justify your answer.

x = yz

Answer 1

A linear equation in a 2 variables is an algebraic equation in which each term has an exponent of one if we graph the equation, we get a straight line. For example ax+by = c , where a,b,c are arbitrary real numbers, is a linear equation in 2 variables.

Similarly, a linear equations in 3 variables is also an algebraic equation in which each term has an exponent of one. For example ax+by +cz= d , where a,b,c,d are arbitrary real numbers, is a linear equation in 3 variables. Here, the equation represents a plane.

The equation x = yz is not a linear equation as it does not conform to the definition of a linear equation.