7.3 – Solving Linear Systems By Linear Combination.

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Presentation transcript:

7.3 – Solving Linear Systems By Linear Combination

Homework Answers  20. (4, -2)  21. (2, 9)  22. (-1, 5)  23. (5, 15)  24. (0, 0)  25. (-3, -3)

Homework Quiz  Show the original problem, your work, and the final answer to problems #21 and #25.

Practicing Standard Form  Put the following equations into standard form!

 In linear combination, we want to change TWO equations with TWO variables into ONE equation with ONE variable. What does Linear Combination mean?

Steps 1.Put equations in STANDARD FORM. 2.Multiply equations to create opposites. 3.Add equations together to create one new equation. 4.Solve for the first variable. 5.Substitute the variable into the easier original equation. 6.Solve for the second variable. 7.Check your answer!

Example 1 (iDo) (4, 0) 1.Put equations in STANDARD FORM. 2.Multiply equations to create opposites. 3.Add equations together to create one new equation. 4.Solve for the first variable. 5.Substitute the variable into the easier original equation. 6.Solve for the second variable. 7.Check your answer!

Example 2 (iDo) (2, 1) 1.Put equations in STANDARD FORM. 2.Multiply equations to create opposites. 3.Add equations together to create one new equation. 4.Solve for the first variable. 5.Substitute the variable into the easier original equation. 6.Solve for the second variable. 7.Check your answer!

Example 3 (iDo) (-0.5, 1.5) 1.Put equations in STANDARD FORM. 2.Multiply equations to create opposites. 3.Add equations together to create one new equation. 4.Solve for the first variable. 5.Substitute the variable into the easier original equation. 6.Solve for the second variable. 7.Check your answer!

Break Time  Take a minute to stretch out, talk to a neighbor, or try the following rebus puzzles… Space invadersForgive and forget

Example 4 (wiiDo) (2, 3) 1.Put equations in STANDARD FORM. 2.Multiply equations to create opposites. 3.Add equations together to create one new equation. 4.Solve for the first variable. 5.Substitute the variable into the easier original equation. 6.Solve for the second variable. 7.Check your answer!

Example 5 (wiiDo) (3, -1) 1.Put equations in STANDARD FORM. 2.Multiply equations to create opposites. 3.Add equations together to create one new equation. 4.Solve for the first variable. 5.Substitute the variable into the easier original equation. 6.Solve for the second variable. 7.Check your answer!

Example 6 (wiiDo) (0, 4) 1.Put equations in STANDARD FORM. 2.Multiply equations to create opposites. 3.Add equations together to create one new equation. 4.Solve for the first variable. 5.Substitute the variable into the easier original equation. 6.Solve for the second variable. 7.Check your answer!

Example 7 (uDo) (-2, 3) 1.Put equations in STANDARD FORM. 2.Multiply equations to create opposites. 3.Add equations together to create one new equation. 4.Solve for the first variable. 5.Substitute the variable into the easier original equation. 6.Solve for the second variable. 7.Check your answer!

Example 8 (uDo) (4, 1) 1.Put equations in STANDARD FORM. 2.Multiply equations to create opposites. 3.Add equations together to create one new equation. 4.Solve for the first variable. 5.Substitute the variable into the easier original equation. 6.Solve for the second variable. 7.Check your answer!

Exit Slip Solve the following systems by linear combination. 1) 2) Can use your notes and textbook To be done individually Must be silent until all exit slips have been collected If you have any questions, write them down on your exit slip (8, -2) (-2, 3)

Tonight’s Homework  pg. 414 #16-24