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Topic 7

Topic 7. Solving systems of equations. 8.3.7 solving systems of equations by graphing. Two or more equations with the same set of variables are called a system of equations. For example, y = 4x and y = 3x + 2 together are a system of equations.

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Topic 7

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  1. Topic 7 Solving systems of equations

  2. 8.3.7 solving systems of equations by graphing • Two or more equations with the same set of variables are called a system of equations. • For example, y = 4x and y = 3x + 2 together are a system of equations. • You can find the solution of a system of equations by graphing the equations on the same coordinate plane. The ordered pair for the point of intersection of the graphs is the solution of the system because the point of intersection simultaneously satisfies both equations.

  3. Number of solutions: • The graph of a system of equations indicates the number of solutions: • If the lines intersect, there is ONE solution. • If the lines are parallel, there is NO solution. • If the lines are the same, there is an INFINITE NUMBER of solutions. Remember: in an ordered pair, the numbers are ALWAYS written (x, y).

  4. 8.3.8 solving systems of equations algebraically • In the previous lesson, you estimated the solution of a system of equations by graphing. • In this lesson, you will use substitution. Substitution is an algebraic model that can be used to find the exact solution of a system of equations.

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