Google Classroom
GeoGebraGeoGebra Classroom

IM Alg1.2.14 Lesson: Solving Systems by Elimination (Part 1)

What do you notice? What do you wonder?



Diego is solving this system of equations:

Here is his work:


Make sense of Diego’s work and discuss with a partner:
  • What did Diego do to solve the system?
  • Is the pair of  and  values that Diego found actually a solution to the system? How do you know?

Does Diego’s method work for solving these systems? Be prepared to explain or show your reasoning.

Here are three systems of equations you saw earlier.

System ASystem BSystem C

For each system:
  • Use graphing technology to graph the original two equations in the system. Then, identify the coordinates of the solution.
  • Find the sum or difference of the two original equations that would enable the system to be solved.  
  • Graph the third equation on the same coordinate plane. Make an observation about the graph.

Mai wonders what would happen if we multiply equations.

That is, we multiply the expressions on the left side of the two equations and set them equal to the expressions on the right side of the two equations. In system B write out an equation that you would get if you multiply the two equations in this manner.

Does your original solution still work in this new equation?

Use graphing technology to graph this new equation on the same coordinate plane.

Why is this approach not particularly helpful?