Solving Systems of Linear EquationsA series of free Intermediate Algebra Video Lessons from Brightstorm online Algebra series.
Solving a System of Linear Equations in Two Variables A system of linear equations is two or more equations that contain the same variables. A solutions to a system of equations are the point where the lines intersect. There are four methods to solving systems of linear equations: graphing, substitution, elimination and matrices. Solving systems of equations first shows up in Algebra I, but more complex applications occur in Algebra II.
Solving a Linear System in Three Variables with a Solution In Algebra II, sometimes we will be asked to solve systems of equations three variables. When solving these systems of equations, a 3D coordinate system is necessary since systems of equations with three variables are not linear. Therefore, solving these systems of equations by graphing is not possible. Solving by substitution would be difficult, so we often solve by addition and elimination.
Solving a Linear System in Three Variables with no or Infinite Solutions Sometimes we have a system of equations that has either infinite or zero solutions. We call these no solution systems of equations. When we solve a system of equations and arrive at a false statement, it tells us that the equations do not intersect at a common point. One scenario is that 2 or more of the planes are parallel or that two of the planes intersect and the other intersects at a different point
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