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If we can solve the equation and get something like x=b where b is a specific number, then we have one solution Determine the number of solutions of a given system of equations by considering its algebraic solution process. If we end up with a statement that's always false, like 3=5, then there's no solution
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If we end up with a statement that's always true, like 5=5, then there are infinite solutions. So an equation with infinitely many solutions essentially has the same thing on both sides, no matter what x you pick. In other words, the equations are equivalent and share the same graph
Any solution that works for one equation will also work for the other equation, so there are infinite solutions to the system.
Practice telling whether an equation has one, zero, or infinite solutions With 2 linear equations, there are 3 possible solution scenarios 1) the 2 lines intersect and the point of intersection is the solution to the system (the one point in common). To have more than one solution and not have infinite solutions, one or both of the equations needs to create a graph that curves
If their graph curves, then they are not linear equations. A dependent system has infinitely many solutions because the equations are multiples of each other, while an independent system has a unique solution Therefore, if a system is inconsistent, it is neither dependent nor independent, as it does not have any solutions at all. And they say identify one system, but we can see here there's actually going to be two systems that have a single solution
And when we talk about a single solution, we're talking about a single x and y value that will satisfy both equations in the system.
If you are asked to calculate when it hits the ground, you will get two solutions, but both of those can't be right, because physically that makes no sense Often in that case you might get one solution with positive time, and one solution at a negative value of time, so that one you'd throw out.
