# Illustrative Mathematics Grade 8, Unit 4, Lesson 14: Solving More Systems

Learning Targets:

• I can use the structure of equations to help me figure out how many solutions a system of equations has.

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Illustrative Math

#### Lesson 14: Solving More Systems

Let’s solve systems of equations.

Illustrative Math Unit 8.4, Lesson 14 (printable worksheets)

#### Lesson 14 Summary

The following diagram show how to solve systems of equations using substitution. #### Lesson 14.1 Algebra Talk: Solving Systems Mentally

Solve these without writing anything down:

#### Lesson 14.2 Challenge Yourself

Here are a lot of systems of equations:

1. Without solving, identify 3 systems that you think would be the least difficult to solve and 3 systems that you think would be the most difficult to solve. Be prepared to explain your reasoning.
2. Choose 4 systems to solve. At least one should be from your “least difficult” list and one should be from your “most difficult” list.

#### Lesson 14.3 Five Does Not Equal Seven

Tyler was looking at this system of equations:
He said,
“Just looking at the system, I can see it has no solution. If you add two numbers, that sum can’t be equal to two different numbers.”
Do you agree with Tyler?

#### Are you ready for more?

In rectangle ABCD, side AB is 8 centimeters and side BC is 6 centimeters. F is a point on BC and E is a point on AB. The area of triangle DFC is 20 square centimeters, and the area of triangle DEF is 16 square centimeters. What is the area of triangle AED? #### Lesson 14 Practice Problems

1. Solve:
y = 6x
4x + y = 7
2. Solve:
y = 3x
x = -2y + 70
3. Which equation, together with y = -1.5x + 3, makes a system with one solution?
4. The system x - 6y = 4, 3x - 18y = 4 has no solution.
a. Change one constant or coefficient to make a new system with one solution.
b. Change one constant or coefficient to make a new system with an infinite number of solutions.
5. Match each graph to its equation.
6. Here are two points: (-3,4), (1,7). What is the slope of the line between them?

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

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