1. 2. Therefore, the equations are equivalent and will share the same graph. Each page includes appropriate definitions and formulas followed by solved problems listed in … This article will use three examples to show that assumption is incorrect. Having no solution means that an equation has no answer whereas infinite solutions of an equation means that any value for the variable would make the equation true. And an expression consists of variables like x or y and constant terms which are conjoined together using algebraic operators. You can put this solution on YOUR website! Hence, a system will be consistent if the system of equations has an infinite number of solutions. The two lines having the same y-intercept and the slope,  are actually the exact same line. 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Definition of Finite set Finite sets are the sets having a finite/countable number of members. https://www.khanacademy.org/.../v/number-of-solutions-to-linear-equations-ex-3 Example of infinite solutions in the simplex algorithm: There are infinite solutions that maximize the objective function in this case the solution provided by the simplex algorithm is finite but it is not unique. An infinite limit may be produced by having the independent variable approach a finite point or infinity. If you multiply line 1 by 5, you get the line 2. If we multiply 5 to equation 1, we will achieve equation 2 and on dividing equation 2 with 5, we will get the exact first equation. Infinite represents limitless or unboundedness. This article reviews all three cases. As you can see, the final row of the row reduced matrix consists of 0. A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line). 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