Check if a point is a solution
Is (0, 0) a solution to the following system:
y=3x
2x+5=y
No!
0=3(0) is true
2(0)+5=0 is not true
Solve the system of equations by graphing:
y=-3x-2
y= 1/2 x+5
(-2, 4)
Solve the system using substitution:
y=2x+7
3x-4y= -13
(-3, 1)
When solving the system below using substitution, which equation should you get x or y by itself? Which variable, x or y, will you get by itself?
x-y= -3
4x-2y=2
First equation, get x by itself
Tickets to a movie cost $5 for adults and $3 for students. A family purchased 18 tickets for $82.00.
How many adult tickets did the family purchase? How many student tickets did the family purchase?
QUESTION: Define your variables. Write a system of equations to represent the situation.
a = # of adult tickets
s = # of student tickets
a+s=18 (total number of tickets)
5a+3s=82 (cost of tickets)
Is (1, 8) a solution to the following system:
y=x+7
3x-y = -5
Yes!
8=1+7 is true
3(1)-8 = -5 is true
Solve the system of equations by graphing:
y=2x+5
3x+y=10
3x+y=10 ---> y=-3x+10
Solution: (1, 7)
Solve the system of equations using substitution:
-4x+8y= -12
y=5x+21
(-5, -4)
Solve the system of equations using substitution:
-4x-2y=8
-2x+y=20
(-6, 8)
At a store, Eva bought two shirts and five hats for $154.00. Nicole bought three shirts and four hats for $168.00.
What is the price of each shirt? What is the price of each hat?
QUESTION: Define your variables. Write a system of equations to represent the situation.
s = price of each shirt
h = price of each hat
2s+5h=154 (Eva's purchase)
3s+4h=168 (Nicole's purchase)
Is (-7, 2) a solution to the following system:
y=x+9
x+2y=4
No!
2=-7+9 is true
-7+2(2)=4 is not true
Solve the system of equations by graphing:
y=x-2
-x+y=4
-x+y=4 ---> y=x+4
Solution: no solution (lines are parallel)
Solve the system of equations using substitution:
x-y=0
y=3x-2
(1, 1)
x+2y=-6
-5x+4y=2
(-2, -2)
A class of 195 students went on a field trip where they took 19 vehicles in total -- some cars and some buses. Each car holds 5 students and each bus holds 25 students.
a) Define your variables. Write a system of equations to represent the situation.
b) How many buses did they take?
c) How many cars did they take?
A) b = # of buses they took, c = # of cars they took
b+c=19 (total vehicles)
5c+25b=195 (number of students taken)
B) 5 buses
C) 14 cars
Is (-2, -5) a solution to the following system:
y=4x+3
5x-2y=0
Yes!
-5=4(-2)+3 is true
5(-2)-2(-5)=0 is true
Solve the system of equations by graphing:
y=-x-4
x-3y=12
x-3y=12 ---> y= 1/3 x-4
Solve the system of equations using substitution:
x=3+2y
4x+2y=12
(3, 0)
Solve the system of equations using substitution:
-3x+y=5
5x-y=-11
(-3, -4)
Tickets to a movie cost $5 for adults and $3 for students. A family purchased 18 tickets for $82.00.
A) Define your variables. Write a system of equations to represent the situation.
B) How many adult tickets did the family purchase?
C) How many student tickets did the family purchase?
A) a = # of adult tickets, s = # of student tickets
a+s=18 (total number of tickets)
5a+3s=82 (cost of tickets)
B) 14 adult tickets
C) 4 student tickets
Is (-1, 6) a solution to the following system:
4x+y=2
5x+3y=20
No!
4(-1)+6=2 is true
5(-1)+3(6)=20 is not true
Solve the system of equations by graphing:
2x+4y=8
4x+8y=16
2x+4y=8 ---> y= -1/2 x+2
4x+8y=16 ---> y=-1/2 x+2
Solution: infinite solutions
NOTE: you still need to graph the system because you are being asked to solve by graphing, not by looking at the equation!
Solve the system using substitution:
y= -8x-24
y=-x+4
(-4, 8)
Solve the system of equations using substitution:
x-2y= -18
3x+5y=1
(-8, 5)
At a store, Eva bought two shirts and five hats for $154.00. Nicole bought three shirts and four hats for $168.00.
A) Define your variables. Write a system of equations to represent the situation.
B) What is the price of each shirt?
C) What is the price of each hat?
A) s = price of each shirt, h = price of each hat
2s+5h=154 (Eva's purchase)
3s+4h=168 (Nicole's purchase)
B) $32
C) $18