Unit 2 Lesson 12

Systems of Equations and Solving

Objectives

• SWBAT graph a system of equations. 

• SWBAT solve systems of equations using algebra.

  
  

1. Plot a point to represent the y-intercept (b)

2. Use the slope to plot another point. (m)

3. Connect the dots.

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​Graph Systems of Equations

y= 3/5x + 2
y= 1/5x + 4

​A stack of n small cups has a height, ℎ, in centimeters of h = 1.5n + 6


A stack of n large cups has a height, ℎ, in centimeters of h = 1.5n + 9

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12.3: Stacks of Cups

Draw

Small Cups: h = 3/2n + 6

Large Cups: h = 3/2n + 9

Graph the equations for each cup on the same set of axes.

Here is a graph that represents the equation for stacking the small cups and an equations for stacking the large cups. Use this to answer the next question.

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12.3: Stacks of Cups

Fill in the Blank

1. For what number of cups will the two stacks have the same height?

13.2: Matching Graphs to Systems

On the next slide is three systems of equations graphed on a coordinate plane

• You will match each figure to one of the systems of equations shown.

Match

Match each figure to one of the systems of equations shown here.

y=3x+5

y=−2x+20

y=0.5x+12

y=2x+27

y=2x−10

y=4x−1

• y=3x+5

  y=−2x+20

• y=0.5x+12

  y=2x+27

• y=2x−10

  y=4x−1

On the next slide you will find the solution to the system of equation.

View the video to see how Mr. Morgan solves!
(Start at 7:34 - 9:30)

13.2: Matching Graphs to Systems

Fill in the Blank

Find the solution and check that your solution is reasonable based on the graph.

(Hint: Make the equations equal to one another, solve for x, and then solve for y. What is the coordinate?)

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,

)

No Solution
One Solution
Infinitely Many Solutions

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13.3 Different Types of Systems