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You use algebra and solve the system(s) of equations using techniques such as elimination or substitution.
Substitution is a way to solve without graphing, and sometimes there are equations that are impossible or very difficult to graph that are easier to just substitute. Mostly though, it is a way to solve if you have no calculator or cannot use one (for a test or worksheet).
coordinate geometry or algebra is used to solve equations
Write your answer as an ordered pair. y = -3 + 5x 3x - 8y = 24
When you are solving a system of linear equations, you are looking for the values for the unknown variables (usually named x and y) that make each equation in the system true. Instead of using algebraic substitution or elimination, you can use graphing to find the variables. If you graph each equation on the same graph, the point where the graphs cross is the answer, which should be given as an ordered pair in the form (x,y). If the graphs do not cross anywhere (for example, parallel lines) then there is no solution. If the graphs of two lines end up being the same line, then there are an infinite number of solutions. You must know how to graph a line in order to use this method.