7.1 Systems of

Linear Equations

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

Systems of Equations – 2 Variables

InconsistentNo Solution

ConsistentIndependentOne Solution

ConsistentDependent

Infinite Solutions

Solve each system by graphing

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

Inconsistent

NoSolution

ConsistentIndepende

ntOne

Solution

ConsistentDependent

InfiniteSolutions

Possible solutions for a system of equations

with 2 variables

Solve each system of equations using the Substitution Method

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

Solve each system of equations using the Elimination Method

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

Solve each system of equations with three

variables

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

The perimeter of a rectangular floor is 208

feet. Find the dimensions of the floor

if the length is three times the width.

Let x Length

Let y Width

P 2l 2w

208 2x 2y

x 3y

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?

Let x Cost of a Cheeseburger

Let y Cost of a Milkshake

4x 2y 20.40

2y 1.2 2x

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.

Rate Time Distance

With x + y 10 2400Against x – y 12 2400

Let x Plane Speed

Let y Wind Speed

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?

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

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?

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