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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!
3 7 4
2 3 1
5 5 8
y x
x y
y x
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)
4x+3y =16
2x-3y =8
(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)
3x+2y =8
2y =12-5x
(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)
3x+5y =6
-4x 2y =5
(-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 invaders Forgive and forget
Example 4 (wiiDo)
122y3x
22y4x
(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)
3x+2y =7
3x+4y =5
(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)
4x+3y =12
12x=8y-32
(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)
5x+2y =-4
-5x 3y 19
(-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)
6x+4y =28
5x-2y =18
(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
2x-4y=24
x+2y=4
-3x+y=9
6x+3y=-3
(8, -2)
(-2, 3)
Tonight’s Homework
pg. 414 #16-24
