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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