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How to Solve Systems of Equations: Methods and Determinants

A system of linear equations is an algebraic problem where the terms consist of constants and variables on both sides of an equal sign and are presented in two or more equations. Linear equations can have more than one variable. The number of variables affects the way that the equation is solved. In general, equations with more than one variable will have a simplified solution with the variables still present. Most problems involve a pair of two equations. The simplest way to identify a linear equation is the presence of "y=" on one side of the equation. When multiple variables are present, you will need a set of linear equations to actually solve the equations because you are trying to find their intersection points.

Instructions

  1. Graphing

    • 1

      Graph the first line onto a x,y axis.

    • 2

      Graph the second line onto the same axis.

    • 3

      Mark the point where they intersect. This is your solution.

    Substitution

    • 4

      Select one of the equations to solve first. This will preferably have a variable with 1 as its coefficient.

    • 5

      Factor the second equation to isolate a single variable on one side.

    • 6

      Replace the isolated variable's value in the first equation to convert it into a single variable problem.

    • 7

      Factor the first equation to solve for its variable then use the value to solve the second equation.

    Canceling

    • 8

      Manipulate the equation so that either "x" or "y" can be cancelled out. This is typically done by multiplying one equation by -1.

    • 9

      Solve by combining the two equations and solve for the remaining variable.

    • 10

      Plug in your answer for the first variable and solve for the other variable.

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