Solving a System of Linear Equations by Graphing
Graph the following system of linear equations to get your solution.
y= -2x + 5
y= 4x-1
(1,3)
Solving the following system of linear equations by using the substitution method.
y= -x+3
3y+5x=-1
(-5,8)
Solving the following system of linear equations by using the elimination method.
2x+2y=4
2x+y=6
(4,-2)
As a fundraiser, the music club sold shirts. They sold a total of 40 shirts. Children’s shirts cost $13 and adult shirts cost $17. If they collected a total of $588 from the sale of the shirts, how many adult shirts were sold?
17 adult shirts were sold
Graph the following system of linear equations to get your solution.
y=1/3x-2
y=-2/3x+4
(6,0)
Solving the following system of linear equations by using the substitution method.
y=3x+14
y=-4x
(2,8)
Solving the following system of linear equations by using the elimination method.
8y-5x=12
-8y+5x= -12
Infinitely Many Solutions
You and a friend go to Tacos Galore for lunch. You order three soft tacos and three burritos and your total bill is $11.25. Your friend's bill is $10.00 for four soft tacos and two burritos. How much do soft tacos cost? How much do burritos cost?
Graph the following system of linear equations to get your solution.
2y=2x-4
y-x=5
No solution
Solving the following system of linear equations by using the substitution method.
x=2y+4
y=2x-8
(4,0)
Solving the following system of linear equations by using the elimination method.
3x − 5y = −6
2x − 3y = −5
(-7,-3)
You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night you made a total of $78.50. You sold a total of 87 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. How many hot dogs were sold and how many sodas were sold?
35 hot dogs and 52 sodas were sold.
Graph the following system of linear equations to get your solution.
y=5
x=2y-8
(2,5)
Solving the following system of linear equations by using the substitution method.
6y-4x=12
y=\frac{2}{3}x+2
Infinitely Many Solutions
Solving the following system of linear equations by using the elimination method.
2x + 3y = 11
5x − 2y = −20
(2,5)
Beth has two dogs. The larger dog weighs 1.4 pounds more than the smaller dog. The combined weight of the two dogs is 12.6 pounds. What is the weight, in pounds, of the smaller dog?
5.6 pounds
Graph the following system of linear equations to get your solution.
y+3x=2(x-2)
4y-2=2+x
(-4,0)
Solving the following system of linear equations by using the substitution method.
2y=4x-2
3x+7y=10
(1,1)
Solving the following system of linear equations by using the elimination method.
−3x + y = 4
−6x + 2y = −2
No solution
A car rental company charges $34 per day for a rented car and $0.50 for every mile driven. A second car rental company charges $20 per day and $0.75 for every mile driven. What is the number of miles at which both companies charge the same amount for a one-day rental?
56 miles