7.4 Applications of Linear Systems
Goals: Choose the best method to solve a system of linear
equations Use a system to model real-life problems
Eligible Content:A1.1.2.2.1 / A1.1.2.2.2
6-5 Applications of Linear SystemsWhen to use each
methodGraphingIf equations are in slope intercept formIf the
problem involves inequalitiesIf numbers are small and easy to
graph
SubstitutionIf there is a variable without a number in front of
it
Linear CombinationsIf all variables have numbers in frontWhich
method is best?2x + 3y = 44x 2y = 8
4x + y = 35x + 5y = 16
y = 2x + 1y = 3x 5 -3x + y = 95x + 2y = 10
y < 7x + 1y x 3
5x 2y = 93x + 2y = 7Linear CombinationsLinear
CombinationsSubstitutionSubstitutionGraphingGraphingWord
ProblemsSlope-Intercept FormStandard FormThere will be two
different situations to compare.
You are given a slope and a y-intercept for each situation.
Write y = mx + b equations.There will be two different things
you are looking for.
All of the numbers will fall into two categories.
Write Ax + By = C equations.Word Problem #1You want to burn 380
calories during 40 minutes of exercise. You burn about 8 calories
per minute inline skating and 12 calories per minute swimming. How
long should you spend doing each activity?
Standard Form
x = inline skatingy = swimming
Calories: 8x + 12y = 380Minutes: x + y = 4025 minutes inline
skating15 minutes swimmingWord Problem #2Selling frozen yogurt at a
fair you make $565 and use 250 cones. A single-scoop cone costs $2
and a double-scoop cone costs $2.50. How many of each type of cone
did you sell?
Standard Form
x = single-scoopy = double-scoop
Money: 2x + 2.50y = 565Cones: x + y = 250120 single-scoop
cones130 double-scoop conesWord Problem #3You have a choice of two
different Internet service companies. Company A charges $12 each
month plus $2 per hour. Company B charges $27 each month plus $.50
per hour. How many hours would you need to use the Internet for the
two companies to be the same?
Slope-Intercept Form
Company Am = 2b = 12y = 2x + 12Company Bm = .50b = 27y = .50x +
2710 hoursWord Problem #4You enroll in a movie club where you earn
points to use toward future rentals. Each new release costs $3 and
earns 5 points. Each regular movie costs $1.50 and earns 3 points.
On your recent rental you paid $12 and earned 22 points. How many
of each type of movie did you rent?
Standard Form
x = new releasesy = regular movies
Money: 3x + 1.50y = 12Points: 5x + 3y = 222 new releases4
regular moviesWord Problem #5A retailer offers two options for
satellite TV service. A customer may buy the dish for $150 and then
pay $25 per month for service. The other option is to rent the dish
for free and pay $35 per month for service. After how many months
will the two companies be the same?
Slope-Intercept Form
Company Am = 25b = 150y = 25x + 150Company Bm = 35b = 0y = 35x +
015 monthsA.Marcus: $22.00, Anisa: $21.65B.Marcus: $21.00, Anisa:
$22.50C.Marcus: $24.00, Anisa: $20.00D.Marcus: $20.75, Anisa:
$22.75FUNDRAISING For a school fundraiser, Marcus and Anisa
participated in a walk-a-thon. In the morning, Marcus walked 11
miles and Anisa walked 13. Together they raised $523.50. After
lunch, Marcus walked 14 miles and Anisa walked 13. In the afternoon
they raised $586.50. How much did each raise per mile of the
walk-a-thon?
PracticePage 367 #5HomeworkWorksheet 6-5 Applications of Linear
Systems Homework #1
