First-Degree Equation in Two Variables
A first-degree equation with two variables whose exponents are 0 or 1 that is expressed in the general form Ax + By + C = 0, where the coefficients A and B are not zero.
A first-degree equation in two variables generally has an infinite number of solutions.
If A = 0 or B = 0 with A + B ≠ 0, then the equation is a first-degree equation with one unknown.
A system of two first-degree equations in two variables can have a single solution, an infinite number of solutions or no solution, depending on the values of their coefficients.
Examples
- The equation "2x − 3y = 12 " is a first-degree equation in two variables.
- The equation "2xy = 24 " is not a first-degree equation in two variables, since the term 2xy is a second-degree term; the sum of the exponents is 2.
- If x is a whole number, the solution set of the equation x + 5y = 10 is {(0, 2), (1, [latex]\frac{9}{5}[/latex]), (2, [latex]\frac{8}{5}[/latex]), ...}