Solving Systems of Linear Equations by Graphing
Solve the system of linear equations by graphing:
y = 2x + 9
y = -x + 6
(-1,7)
Solve the system of linear equations by substitution:
y = x - 4
y = 4x - 10
(2,-2)
Solve the system of linear equations by elimination:
x + 3y = 5
-x - y = -3
(2,1)
Solve the system of linear equations:
y = 2x - 2
y = 2x + 9
No solution.
Solve the equation:
5(2 - y) + y = -6
y = 4
The high school drama club is selling tickets to their spring musical. On opening night, they sell 3 adult tickets and 2 student tickets, bringing in a total of 22. The next night, popularity grows, and they sell 5 adult tickets and 4 student tickets for a total of 38.
Write a system of equations that models this situation.
2a +3s = 22
5a + 4s= 38
Solve the system of linear equations by graphing:
y = x + 4
y = -x + 2
(-1,3)
Solve the system of linear equations by substitution:
y = 2x + 5
y = 3x - 1
(6,17)
Solve the system of linear equations by elimination:
x - 2y = -7
3x + 2y = 3
(-1,3)
Solve the system of linear equations:
y = 3x + 1
-x + 2y = -3
(-1,-2)
Write the equation in standard form:
3x - 9 = 7y
3x - 7y = 9
Maya is buying a new tablet and a heavy-duty protective case for school. The store clerk tells her that the protective case is 25 less than half the price of the tablet. The total cost for both items together before tax is 350.
Write a system of equations that models this situation.
c=.5tâ25
c+t= 350
t=tablet
c=case
Solve the system of linear equations by graphing:
y = 2x + 5
y = 0.5x - 1
(-4,-3)
Solve the system of linear equations by substitution:
x = 2y + 7
3x - 2y = 3
(-2, -4.5)
Solve the system of linear equations by elimination:
2x + 7y = 1
2x - 4y = 12
(4,-1)
Solve the system of linear equations:
y = 5x - 9
y = 5x + 9
No solution.
Write the equation of the line that passes through the points (-1, 6) and (2, 0) in slope-intercept form.
â2x+4=y
A farmer looks out into his yard and counts a total of 15 animals, consisting entirely of chickens and goats. If the farmer counts a total of 44 legs among all the animals, how many chickens and how many goats does he have? Create a system of equations to represent this scenario.
x+y=15
2x+4y=44
x=Chickens
y=Goats
Solve the system of linear equations by graphing:
x + y = 7
y = x + 3
(2,5)
Solve the system of linear equations by substitution:
2x = y - 10
x + 7 = y
(-3,4)
Solve the system of linear equations by elimination:
2x - y = 0
3x - 2y = -3
(3,6)
Solve the system of linear equations:
y = 8x - 2
y - 8x = -2
Infinitely many solutions.
Write an equation of the line that passes through the given points:
(0,0) and (2,6)
y = 3x
Marcus goes to a local coffee shop to buy breakfast for his coworkers. He notices that the price of a breakfast sandwich is 2 less than three times the price of a large iced coffee. He decides to buy 2 large iced coffees and 3 breakfast sandwiches, and his total bill comes out to 38.
Determine the exact cost of one iced coffee and one breakfast sandwich.
Coffee = 4
Sandwich =10
Is it possible for a system of linear equations to have exactly two solutions? Explain your reasoning.
No, two lines cannot intersect in exactly two points.
Solve the system of linear equations by substitution:
y - x = 0
2x - 5y = 9
(-3,-3)
Solve the system of linear equations by elimination:
x + 4y = 1
3x + 5y = 10
(5,-1)
Describe and correct the error in solving the system of linear equations.
y = -2x + 4
y = -2x + 6
The lines have the same slope so there are infinitely many solutions.
The lines have the same slope but different y-intercepts so therefore they are never going to intersect = No Solution.
When solving a system of linear equations algebraically, how do you know when the system has no solution?
When solving a system of linear equations algebraically, how do you know when the system has infinitely many solutions?
When solving a system of linear equations algebraically, you know the system has no solution when you reach an invalid statement such as -3 = 2.
Infinitely many solutions has a valid statement such as 1 = 1.
Context:
3 apples and 2 oranges cost 7.
1 apple and 4 oranges cost 9.
Your Task:
Write a system of equations and use elimination to find the cost of 1 apple and 1 orange.
apple= 1
Orange=2