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Solving the system by elimination results in a single ordered triple x y.
Systems of equations with 3 variables. The solution still represents the values for x y and z or whatever variables your equations are using that when plugged into each. The steps include interchanging the order of equations multiplying both sides of an equation by a nonzero constant and adding a nonzero multiple of one equation to another equation. When we had two variables we reduced the system down to one with only one variable by substitution or addition. Independent systems have a single solution.
Three variable systems of equations aren t so different. Graphically the solutions. Systems of equations 3 variables solving systems of equations with 3 variables is very similar to how we solve sys tems with two varaibles. With three variables we will reduce the system down to one with two variables usually by.
Dependent systems have an infinite number of solutions. A system of three equations in three variables can be solved by using a series of steps that forces a variable to be eliminated. When solving systems of equation with three variables we use the elimination method or the substitution method to make a system of two equations in two variables.
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