Download 03-28-17 Substitution Notes

3/28/2017
Prebell
Find the solution to the system below:
−36 = −𝑥 + 6𝑦
−2𝑦 = 𝑥 − 12
a. 3, −9
b. 18, −3
c. −9, 3
d. (−9, −3)
Practice
Prebell
Find the solution to the system of equations.
𝑦 = 𝑥 − 24
𝑦 = −3𝑥
A. (6, 18)
B. 18, 6
C. 6, −18
D. (6, 1)
−2𝑦 = −3𝑥 + 2
−3𝑥 = −4 − 2𝑦
Solve each system by
graphing.
1.
−2𝑦 = −3𝑥 + 2
−3𝑥 = −4 − 2𝑦
2.
𝑥 + 2𝑦 = −6
𝑥 − 𝑦 = −3
𝑥 + 2𝑦 = −6
𝑥 − 𝑦 = −3
Graphing Systems Scavenger Hunt
• You need a ruler, an answer sheet, and a partner
(optional).
• Pick a random problem to start at. Write that problem
number in the top left circle on your answer sheet.
• Copy down the system and return to your desk to work
and graph.
• WRITE YOUR ANSWER ON YOUR ANSWER SHEET!
• When you have an answer, go back to the card to see
which problem you should go to next.
• When you are finished with your 6th problem, it should
send you back to where you started.
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Solving Systems by
Substitution
• Another method for solving systems of
equations.
• Most useful when the solution involves
fractions, decimals, or large numbers.
• Substitution – when you plug in the value of
one variable into an equation and solve for
the other variable.
If one variable has already been solved
for, use it!
𝑥 = 5𝑦 + 3
2𝑥 + 4𝑦 = −1
• Substitute value of x
into other equation.
• Solve for y.
Substitution
• Solve one equation for a variable. What do you
need to cancel to isolate the variable?
– Look for a variable that has already been isolated.
Ex:
𝑥 = 9 − 4𝑦
13𝑥 + 12 = 𝑦
– Look for a variable with a coefficient of +1.
Ex:
𝑥 + 2𝑦 = 14
3𝑥 + 𝑦 = 8
𝑥 − 𝑦 = 11
• Replace that variable with its value in the 2nd
equation. Use parentheses!
𝑥 = 5𝑦 + 3
2𝑥 + 4𝑦 = −1
• Plug your solution into
one of the equations in
the system.
• Evaluate to solve for x.
• Write your answer as an
ordered pair.
If both equations are equal to y, then
you can set both equations equal to
one another and solve for x.
𝑦 = −3𝑥
−4𝑥 + 4𝑦 = 16
𝑦 = −5𝑥
𝑦 = −3𝑥 − 10
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Exit Card
Solve each system using substitution.
1.
𝑦 = −2𝑥
𝑦 = −8𝑥 − 12
2.
𝑦 = −5𝑥
−10𝑥 − 2𝑦 = 0
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