The aim of using the elimination method is to have one variable cancel out. A check using x = 3 and y = 5 in both equations will show that the solution is the ordered pair (3, 5).Īnother way to solve a system of equations is by using the elimination method.
Then, substitute y = 5 into your rewritten equation to find x. Next, substitute (−3 y + 18) in for x into the other equation. Solve the following system of equations by substitution. The solution to the system of equations is always an ordered pair. Then replace that variable in the other equation with the terms you deemed equal and solve for the other variable, y. To solve a system of equations by substitution, solve one of the equations for a variable, for example x. When an exact solution is necessary, the system should be solved algebraically, either by substitution or by elimination. At times the point of intersection will need to be estimated on the graph. Graph each line and determine where they cross.Ī graphic solution to a system of equations is only as accurate as the scale of the paper or precision of the lines. Solve the system of equations graphically.
This is an example of a dependent system of equations. Two equations that actually are the same line have an infinite number of solutions. An inconsistent system of equations has no solution. They are an example of an inconsistent system of equations. They have the same slope and different y-intercepts. The place(s) where they cross are the solution(s) to the system. Lines that cross at a point (or points) are defined as a consistent system of equations. The solution is the ordered pair(s) common to all lines in the system when the lines are graphed. The solution to a system of linear equations is the ordered pair (or pairs) that satisfies all equations in the system. There are three ways to solve a system of linear equations: graphing, substitution, and elimination.
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