Lesson 14

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solving Systems of Equations

Warm Up

Lesson

Summary

Cool

Down

Reflections

Student

Task

Learning

Targets

Practice Problems

Lesson Video

Unit 5

linear relationships

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14.1 Warm Up - true or false: two lines

Use the lines to decide whether each statement is true or false. Be prepared to explain your reasoning using the lines.

1. A solution to 8 = -x + 10 is 2.
2. A solution to 2 = 2x + 4 is 8.
3. A solution to -x + 10 = 2x + 4 is 8.
4. A solution to -x + 10 = 2x + 4 is 2.
5. There are no values of x and y that make y = -x + 10 and y = 2x + 4 true at the same time.

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Learning Targets

• I can graph a system of equations.
• I can solve systems of equations using algebra.

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The purpose of this lesson is to connect algebraic and graphical representations of systems.

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14.2 matching graphs to systems

2. Find the solution to each system and check that your solution is reasonable based on the graph.

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14.3 different types of systems

Your teacher will give you a page with some systems of equations.

1. Graph each system of equations carefully on the provided coordinate plane.
2. Describe what the graph of a system of equations looks like when it has . . .
1. 1 solution�
2. 0 solutions�
3. infinitely many solutions

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Lesson Summary

Sometimes it is easier to solve a system of equations without having to graph the

equations and look for an intersection point. In general, whenever we are solving a system of equations written as

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we know that we are looking for a pair of values that makes both equations true. In

particular, we know that the value for will be the same in both equations. That means that

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For example, look at this system of equations:

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Since the value of the solution is the same in both equations, then we know

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We can solve this equation for :

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Lesson Summary, Cont.

But this is only half of what we are looking for: we know the value for x, but we need the

corresponding value for y. Since both equations have the same y value, we can use either

equation to find the y-value:

y = 2(-2) + 6

OR

y = -3(-2) - 4

In both cases, we find that y = 2. So the solution to the system is (-2,2). We can verify this by graphing both equations in the coordinate plane.

In general, a system of equations can have:

• No solutions. The lines never intersect.
• Exactly one solution. The lines intersect in exactly one point.
• An infinite number of solutions. The graphs of the two equations are the same line!

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Cool Down: two lines

1. Given the lines shown here, what are two possible equations for this system of equations?

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• How many solutions does this system of equations have? Explain your reasoning.

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Reflections

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• Can I graph a system of equations?
• Can I solve systems of equations using algebra?

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Practice Problems

Must do: All problems

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Lesson Video

Part 1

Part 2

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