Download 37-Systems algebraically

CC Algebra
Ms. Socci-pd
___
Name: ____________________
Date: ____________________
Lesson 37-Systems of Equations Algebraically
Do Now:
1) Here is a system of two linear equations. Graph both in the calculator and verify
that the solution to this system is (𝟑, 𝟒), by looking at the table and using the
intersect key.
Equation 1: 𝒚 = 𝒙 + 𝟏
Equation 2: 𝒚 = −𝟐𝒙 + 𝟏𝟎
2) Which equation represents the line that passes through the points
1
(1) y  2 x  9
(3) y 
x8
2
1
(2) y  2 x  3
(4) y 
x6
2
and

There are 2 methods for solving systems algebraically.

They are ___________________ and _____________________.
?
Method 1: Substitution
Solve this system of equations using
substitution. Check.
𝑦 =𝑥+1
𝑦 = −2𝑥 + 10.
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2) Solve and check using the substitution method.
y=x+5
y = 2x + 2
3) Solve and check using the substitution method.
x = -y + 1
x + 3y = 9
Method 2: Elimination
2x + y = 6
x – 3y = -11
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4) Solve the following system of equations.
5) Solve the following system of equations.
𝒙− 𝒚 = 𝟏
𝟐𝒙 + 𝟑𝒚 = 𝟕
𝟑𝐱 + 𝟐𝐲 = 𝟒
𝟒𝐱 + 𝟕𝐲 = 𝟏
6) Solve the following system of equations.
x + 2y = 10
x+y=6
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7) A cellular telephone company has two plans. Plan A charges $11 a month and $0.21 per minute. Plan B
charges $20 a month and $0.10 per minute. After how much time, to the nearest minute, wills the cost
of plan A be equal to the cost of plan B?
8) Some coins (dimes and nickels) are in a pile. The total value of the pile is $1.35. The number of nickels
is one coin less than twice the number of dimes. Using a system of equations, find the number of each
type of coin.
9) Bill has $2.00 in quarters and dimes. The number of quarters is 4 less than twice the number of dimes.
Find the number of coins of each type.
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10) Donna wants to make trail mix made up of almonds, walnuts and raisins. She wants to mix one part
almonds, two parts walnuts, and three parts raisins. Almonds cost $12 per pound, walnuts cost $9 per
pound, and raisins cost $5 per pound. Donna has $15 to spend on the trail mix. Determine how many
pounds of trail mix she can make.
11) The owner of a movie theater was counting the money from 1 day’s ticket sales. He knew that a total of
150 tickets were sold. Adult tickets cost $7.50 each and children’s tickets cost $4.75 each. If the total
receipts for the day were $891.25, how many of each kind of ticket were sold?
12) Sharu has $2.35 in nickels and dimes. If he has a total of thirty-two coins, how many of each coin does
he have?
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13) Using only 32-cent and 20-cent stamps, Charlie put $3.36 postage on a package he sent to his sister. He
used twice as many 32-cent stamps as 20-cent stamps. Determine how many of each type of stamp he
used.
14) A total of 600 tickets were sold for a concert. Twice as many tickets were sold in advance than were
sold at the door. If the tickets sold in advance cost $25 each and the tickets sold at the door cost $32
each, how much money was collected for the concert?
15) A ribbon 56 centimeters long is cut into two pieces. One of the pieces is three times longer than the
other. Find the lengths, in centimeters, of both pieces of ribbon.
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16) The ninth graders at a high school are raising money by selling T-shirts and baseball caps. The number
of T-shirts sold was three times the number of caps. The profit they received for each T-shirt sold was
$5.00, and the profit on each cap was $2.50. If the students made a total profit of $210, how many Tshirts and how many caps were sold?
Elimination Method
1. Rewrite the equation so that x, y, =, # are lined up.
2. IF NECESSARY, Multiply both equations by the numbers that will eliminate x.
AKA Flip Flop
3. Add two equations together.
4. Solve for y variable.
4. Substitute solved value into first equation to solve for x.
5. Check x and y values by substituting into second equation.
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