Section 1
Systems of Equations in Two Variables
By Boundless
A system of equations consists of two or more equations with two or more variables, where any solution must satisfy all of the equations in the system at the same time.
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A simple way to solve a system of equations is to look for the intersecting point or points of the equations. This is the graphical method.
The substitution method is a way of solving a system of equations by expressing the equations in terms of only one variable.
The elimination method is used to eliminate a variable in order to more simply solve for the remaining variable(s) in a system of equations.
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For linear equations in two variables, inconsistent systems have no solution, while dependent systems have infinitely many solutions.
Systems of equations can be used to solve many real-life problems in which multiple constraints are used on the same variables.