He can think of two ways to eliminate a variable and solve the system:
Multiply 4p+2q=62 by 2, then subtract 8p-q=59 from the result.
Multiply 8p-q=59 by 2, then add the result to 4p+2q=62.
Do both strategies work for solving the system?
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4.
Andre and Elena are solving this system of equations:
Andre's first step is to write: 3x=9x-30
Elena’s first step is to create a new system:
Do you agree with either first step?
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5.
Select all systems that are equivalent to this system:
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6.
Here is a system of equations with a solution:
Write a system of equations that is equivalent to this system. Describe what you did to the original system to get the new system.
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7.
Here is a system of equations with a solution:
Explain how you know the new system has the same solution as the original system.
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12.
Here is a system of linear equations:
Find at least one way to solve the system by substitution and show your reasoning.
How many ways can you find?
(Regardless of the substitution that you do, the solution should be the same.)
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13.
Here is a system of equations:
Write an equation that results from subtracting the two equations.
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14.
A grocery store sells bananas for b dollars a pound and grapes for g dollars a pound. Priya buys 2.2 pounds of bananas and 3.6 pounds of grapes for $9.35. Andre buys 1.6 pounds of bananas and 1.2 pounds of grapes for $3.68.
This situation is represented by the system of equations:
Explain why it makes sense in this situation that the solution of this system is also a solution to 3.8b+4.8g=13.03.
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This lesson is from Illustrative Mathematics. Algebra 1, Unit 2, Lesson 16. Internet. Available from https://curriculum.illustrativemathematics.org/HS/teachers/1/2/16/index.html ; accessed 26/July/2021.
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