Solving Systems by Graphing (Topic 26)
y = x - 3
x + 2y = 12
(6, 3)
What variable should you eliminate in the following system and how?
-9x - 4y = 20
x + 4y = 12
Add to eliminate y.
Is substitution a good method for solving this system of equations? Why?
-2y - 10 = x
-10x - y = -14
Yes, because the first equation is equal to x.
Identify the variables in this scenario:
Anthony runs a farm stand that sells apples and strawberries. Each pound of apples sells for $2 and each pound of strawberries sells for $3. Anthony made $80 from selling a total of 35 pounds of apples and strawberries.
x = number of pounds of apples sold
y = number of pounds of strawberries sold
True or False:
Systems of equations can only be a maximum of two equations and have a maximum of two variables.
False
Find the solution to the system of equations:
y = -4x + 4
y = 3/2x + 4
(0, 4)
This system isn't ready to use elimiation. What would the system look like once it's ready to use elimination?
15x - 4y = -50
3x - 2y = -16
15x - 4y = -50
6x - 4y = -32
What would the equation look like after only the first step in the substitution process?
2x + 3y = 4
y = 5x - 27
2x + 3(5x - 27) = 4
Write a system of equations for the following scenario:
Marques will earn $30 every time one of his songs is played in a commercial and he will earn $120 every time one of his songs is played in a movie. Marques' songs were played on 5 more commercials than movies, and his total earnings on the royalties from all commercials and movies was $900.
30x + 120y = 900
x = y + 5
Which of the following is a solution to the system of inequalities?
y < -2x - 6
y > x + 2
a) (1, 2)
b) (-7, -3)
c) (-2, 2)
d) (-4, -5)
B
Identify the solution(s) to this system of equations:
y = 2x - 13
y = x^2 - 6x + 3
(4, -5)
Find the x-value of the system of equations:
8x + 4y = -24
-5x + 4y = -11
x = -1
Find the x-value of the system of equations:
y = 8x + 1
y = 6x + 3
x = 1
Write a system of equations for this scenario:
Francesca is blocking off several rooms in a hotel for guests coming to her wedding. The hotel can reserve small rooms that can hold 2 people, and large rooms that can hold 5 people. Francesca reserved twice as many small rooms as large rooms, which altogether can accommodate 63 guests.
x = 2y
What is the name for this formula?
b^2 - 4ac
The Discriminant
Complete the following statement about this system of equations:
5x + 2y = 36
y = -5/2x + 9
"This system has ________ solutions because ______"
Solve the system of equations using elimination:
7x - 2y = -12
-x + 2y = 0
(-2, -1)
Solve the system of equations using substitution:
-6x + 8y = -18
y = 3x
(-1, -3)
When two numbers are multiplied, they equal 204. When they are subtracted, they equal 5.
What are the two numbers?
17 and 12
(or -17 and -12)
What is the axis of symmertry of the following quadratic function?
y = 3x^2 + 24x + 42
x = -4
Which system of equations has infinitely many solutions?
a) y = x - 7
y = -1.5x - 2
b) 5x + y = -2
-5x - y = -1
c) -3x + y = 2
-6x + 2y = 4
d) y = -7x + 6
y = -10x
C
Solve the system of equations using elimination:
−2x − 5y = −15
−9x + 15y = - 30
(5, 1)
Solve the system of equations using substitution.
x + y = 4
-5y + 2x = 15
(5, -1)
A small town has two local high schools. High School A currently has 800 students and is projected to grow by 80 students each year. High School B currently has 950 students and is projected to grow by 70 students each year. When will the high schools have the same number of students?
15 years
Write an equation for a quadratic function that opens up and has a vertex at (5, 11).
y = (x - 5)^2 + 11