I CAN solve a system using the graphing calculator



I CAN solve a system using the graphing calculator

• Graphing is best when both equations are solved for the same variable

• Using a graph, the solution to a system of equations is where is the point where the lines ___________________

Step 1: Hit y=. Enter the first equation into Y1 and the next into Y2. Use the picture below for reference.

Step 2: Press ZOOM(the middle button on top), then Option 6: ZStandard – this will set up the window to have standard axes.

Step 3: Press GRAPH (the button at the top right) to bring up the graph. See the picture below (our will look a bit different)

Step 4: Press 2ND, then the TRACE button (on the top row) to bring up the CALC menu (Display 7)

Step 5: Select option 5: intersect, then hit the ENTER button three times. Your screen should look like the picture below, with the point of intersection listed at the very bottom of the screen

|Step 1 |Step 3 |Step 4 |Step 5 |

|[pic] |[pic] |[pic] |[pic] |

Practice #1: Practice #2: Practice #3

Solution=_(0.4, 1.2)____ Solution=__No Solution________ Solution=__Infinite solutions_

I CAN solve a system using substitution

• The SUBSTITUTION method is best when one of the variables is already __________________

• Look for the variable that is ALL BY ITSELF. Then substitute into the other equation

Practice #1 Practice #2:

[pic] [pic]

Answer: Answer:

Substitute for x Substitute for y

[pic] [pic]

Then solve for x Then solve for y

[pic] [pic]

[pic] [pic]

I CAN solve systems using linear combinations

• MAGIC PAIR: when coefficients on the same variable are ________________________

• Look for the MAGIC PAIR and __________ the equations together

• If the linear combination method is best when we can make a ______________________ by multiplying both sides of the equation by a constant

Pratice #1: Practice #2:

[pic] [pic]

Add the equations multiply the bottom by -2 and add the equations

[pic] [pic] [pic]

Solve for x [pic] [pic]

[pic] [pic]

[pic] [pic]

Practice #3

[pic]

Multiply both equations to eliminate a variable

Solution is [pic]

I CAN determine the best method to solve a system to solve a word problem

• Identify the two unknowns and write two equations from the word problem

• Pick the best method for solving and solve

Practice #1

Five times a number minus twice another number equals negative one. The sum of the two numbers is negative 3. What the numbers?

Write the system: [pic] solve to get: [pic]

Practice #2

The library sells 376 books at its annual used-book fundraiser. They take in a total of $2120. Children's books cost $4, and adult books cost $7. How many adult books did they sell, how many children’s did they sell?

Write the system: [pic]

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[pic]

[pic]

[pic]

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