All about Systems of Equations
Solving Systems of Linear Equations: Graphing
Solving Systems of Linear Equations: Substitution1
Solving Systems of Linear Equations: Substitution2
How Many Solutions?
100
The Town Recreation Department ordered a total of 100 baseballs and bats for the summer
baseball camp. Baseballs cost $4.50 each and bats cost $20 each. The total purchase was
$822. How many of each item was ordered?
x + y = 100
4.50x + 20y = 822
100
14) What is the solution to the system of linear equations?
(2,2)
100
If we were to do substitution and have a graph of the same system of equations would we get the same solution?
Yes.
Every equation graphs a specific line so no matter how you solve, you get the same solution!
(Graphs are definitely easier, but we don't always have graphed systems!)
100
Solve the systems of equations using substitution:
y=3x-10
x=2
(2,-4)
100
How many solutions does the system of linear equations have?
One! (-4,-6)
200
A group of 40 children attended a baseball game on a field trip. Each child received either
a hot dog or bag of popcorn. Hot dogs were $2.25 and popcorn was $1.75. If the total bill
was $83.50, how many hotdogs and bags of popcorn were purchased?
x + y = 40
2.25x + 1.75y = 83.50
200
What is the solution?
(-1,1)
200
What is the first step when solving a system of linear equations using the SUBSTITUTION method?
Isolate the variable
200
Solve the systems of equations using substitution:
y=2x-10
y=4x+8
(-9,-28)
200
How many solutions does the system of linear equations have?
y = 3x - 5
y = 3x + 7
Zero or None
300
Adult tickets for the school musical sold for $3.50 and student tickets sold for $2.50. On a
given night, 321 tickets were sold for $937.50. How many of each kind of ticket were sold?
x + y= 321
3.50x + 2.50y = 937.50
300
Solve Using Graphing:
y = 5/3x + 2
y = -3
300
What is your new (one) equation after performing substitution?
y=2x
3x+y=20
3x+(2x)=20 or
5x=20
300
Solve the systems of equations using substitution:
y = -2x - 9
3x -6y = 9
(-3, -3)
300
How many solutions does the system of linear equations have?
y = (-5/3)x + 3
y = (1/3)x - 3
One
400
One night a theater sold 548 movie tickets. An adult’s ticket costs $6.50 and a child’s ticket
cost $3.50. In all, $2881 was taken in. How many of each kind of ticket were sold?
x + y = 548
6.50x + 3.50y = 2881
400
Solve the systems of linear equations by graphing:
400
How would you isolate x in this equation?
6y+x=20
subtract 6y from both sides to get:
x=20-6y
400
Solve the systems of equations using substitution:
2x - y = 6
x = y + 5
(1, -4)
400
How many solutions does the system of linear equations have?
y = 3x + 9
2y = 6x + 18
Infinitely many solutions
500
How do we write solutions to systems of linear equations?
(x,y)
500
Solve this by graphing:
2x - y = 4
x + 3y = 3
(3,2)
500
Use the substitution method to solve the system of linear equations:
y=2x
3x+y=20
Solution: (4,8)
500
Use the Elimination method to solve the system of linear equations:
−8x − 10y = 24
6x + 5y = 2
(7,-8)
500
How many solutions does the system of linear equations have?
y = 2x - 5
4y = 8x - 5
Zero or None