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7.1 Systems of
Linear Equations
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Graphing Method
Reminders1.Write each equation in slope-
intercept form
2.Graph each line on the coordinate plane
3.Label your lines
4.Identify the solution for the system
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Systems of Equations – 2 Variables
InconsistentNo Solution
ConsistentIndependentOne Solution
ConsistentDependent
Infinite Solutions
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Solve each system by graphing
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Substitution MethodReminders – 2
Equations1.Solve either equation for one variable
in terms of the other
2.Substitute for that variable into the other equation and solve
3.Substitute your answer into either of the original equations to find the value of the other variable
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Inconsistent
NoSolution
ConsistentIndepende
ntOne
Solution
ConsistentDependent
InfiniteSolutions
Possible solutions for a system of equations
with 2 variables
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Solve each system of equations using the Substitution Method
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Elimination MethodReminders – 2
Equations1. Eliminate either variable
2. Find the additive inverse of one variable by multiplying either/both equations by a constant
3. Add the two equations vertically
4. Solve for one variable and substitute the value of the variable into either of the original equations
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Solve each system of equations using the Elimination Method
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Reminders – 3 Equations
1. Pair any 2 equations and eliminate one variable
2. Pair any 2 other combination of equations and eliminate the same variable
3. Solve your new system for one variable
4. Substitute the value of the variable into either one of the previous equations and solve for the other variable
5. Plug the value of the 2 variables into either one of the original equations to find the third variable
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Solve each system of equations with three
variables
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Linear Word ProblemsReminders
1.Identify your variables
2.Set up a table when appropriate
3.Set up a system of equations and solve
4.Write the solution to the system in a sentence answering the given question
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The perimeter of a rectangular floor is 208
feet. Find the dimensions of the floor
if the length is three times the width.
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Let x Length
Let y Width
P 2l 2w
208 2x 2y
x 3y
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Four cheeseburgers and two chocolate
shakes cost a total of $20.40. Two shakes
cost $1.20 more than two cheeseburgers. What is the cost of a
cheeseburger? What is the cost of a chocolate
shake?
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Let x Cost of a Cheeseburger
Let y Cost of a Milkshake
4x 2y 20.40
2y 1.2 2x
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With a tail wind, a small Piper aircraft can
fly 2400 miles in 10 hours. Against this
same wind, the Piper can fly the same
distance in 12 hours. Find the average wind speed and the average air speed of the Piper.
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Rate Time Distance
With x + y 10 2400Against x – y 12 2400
Let x Plane Speed
Let y Wind Speed
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A doctor’s prescription calls for a daily intake containing 40mg of vitamin C and 30mg of vitamin D. Your pharmacy stocks two compounds that can be used: one contains 20% vitamin C and 30% vitamin D, the other 40%
vitamin C and 20% vitamin D. How many mgs of each
compound should be mixed to fill the prescription?
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Let x #of mg of Compound 1
Let y #of mg of Compound 2
0.2x 0.4y 40 Vitamin C
0.3x 0.2y 30 Vitamin D
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A movie theater charges $8.00 for adults, $4.50 for children, and $6.00 for senior citizens. One
day the theater sold 405 tickets and collected
$2320 in receipts. There were twice as many
children’s tickets sold as adult tickets. How many
adults, children, and senior citizens went to the theater that day?
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Let x #of Adult Tickets
Let y #of Children Tickets
Let z #of Senior Citizen Tickets
x y z 405
8x 4.5y 6z 2320
y 2x