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Systems of Equations (Substitution)




 


Videos and lessons to help Grade 8 students learn how to analyze and solve pairs of simultaneous linear equations.

A. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

B. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

C. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

Common Core: 8.EE.8ab

Suggested Learning Targets


  • I can identify the solution(s) to a system of two linear equations in two variables as the point(s) of intersection of their graphs.
  • I can describe the point(s) of intersection between two lines as the points that satisfy both equations simultaneously.
  • I can define "inspection."
  • I can solve a system of two equations (linear) in two unknowns algebraically.
  • I can identify cases in which a system of two equations in two unknowns has no solution.
  • I can identify cases in which a system of two equations in two unknowns has an infinite number of solutions.
  • I can solve simple cases of systems of two linear equations in two variables by inspection.
  • I can estimate the point(s) of intersection for a system of two equations in two unknowns by graphing the equations.
  • I can represent real-world and mathematical problems leading to two linear equations in two variables.

Related Topics:
Common Core for Grade 8

Common Core for Mathematics

More Math Lessons for Grade 8

In this lesson you will learn to solve simple systems of linear equations by trial and error.


In this lesson you will learn how to solve a system of linear equations by substitution.





Solve systems of equations using substitution (1).
In this lesson, you will learn how to solve systems of equations algebraically by substitution when one of the equations is in slope-intercept form.


Solve systems of equations using substitution (2).
In this lesson, you will learn how to solve systems of equations algebraically by substitution when both of the equations is in slope-intercept form.



 

Solving Linear Systems of Equations Using Substitution.
3 complete examples are shown along with an outline of the basic idea.


Solve a System of Equations Using Substitution.
This video provides an example of how to solve a system of linear equation using the substitution method.





Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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