Question

Construct a linear equation in two variables, namely x and y such that (I) Coefficient of x is - 3 (II) Coefficient of y is 1 (III) It passes through the origin. The equation is. Single choice.


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Answer 1

The coefficients may be considered as parameters of the equation, and may be arbitrary expressions, provided they do not contain any of the variables. To yield a meaningful equation, the coefficients displaystyleldots 1, \ldots, are required to not all be zero.

Alternatively a linear equation can be obtained by equating to zero a linear polynomial over some field, from which the coefficients are taken.

The solutions of such an equation are the values that, when substituted for the unknowns, make the equality true.