Solving Systems of Equations with Linear Combinations


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question 1 of 3

Which ordered pair is a solution to this system of equations:

2x + y = 2

x - y = 4

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1. In our lesson, what two KEY properties were used to help prove that a solution is the same regardless of how we combine linear equations?


Given the system of equations:

4x - 5y = 23 (Equation C)

3x + 10y = 31 (Equation D)

If Equation C was multiplied by 2 on each side of the equation, which variable would be eliminated?

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About This Quiz & Worksheet

Use these study resources to determine how much you know about the solutions to equation combinations. You'll be responsible for answering a question on an ordered pair as a solution to given equations, and you should be able to prove that a solution is the same no matter how the linear equations are combined.

Quiz & Worksheet Goals

These topics will be addressed:

  • The elimination of a variable in a system of equations
  • How to solve a system of equations with a linear combination
  • A system of equations with x, y variables that result in a positive and negative number that is the same but opposite

Skills Practiced

  • Critical thinking - apply relevant concepts to examine information about equation combinations in a different light
  • Problem solving - use acquired knowledge to solve linear combination practice problems
  • Knowledge application - use your knowledge to answer questions about solving a system of equations using linear combination

Additional Learning

For more on the mathematics of solving linear equations, review the lesson we've named Solving Systems of Equations with Linear Combinations. Topics in the lesson are listed as follows:

  • What it means in mathematics to have something in common
  • How to define systems of linear equations
  • The use of substitution and graphing when solving a system of linear equations