Graphing
Two lines have the same slope but different y-intercepts.
How many solutions does the system have?
No Solution (parallel lines)
Solve:
y = 3x
2x + y = 8
(2, 6)
Solve:
x + y = 7
x - y = 1
(4, 3)
The sum of two numbers is 10. Their difference is 2. Find the numbers.
6 and 4
Is (2,1) a solution to:
y ≥ x - 1
y < 3
yes
Two lines have different slopes.
How many solutions does the system have?
One Solution
Solve:
y = x + 5
3x - y = 7
(6, 11)
Solve:
2x + y = 10
3x - y = 5
(3, 4)
A movie ticket costs $8 for students and $10 for adults.
5 tickets cost $46 total.
How many adult tickets were sold?
3 adult tickets
Is (0,4) a solution to:
y ≤ -2x + 5
y > 1
yes
Two equations represent the exact same line.
How many solutions does the system have?
Infinitely Many Solutions
Solve:
x = 4 - y
2x + y = 5
(1, 3)
Solve:
3x + 2y = 16
5x - 2y = 4
(2, 5)
You buy 3 pencils and 2 notebooks for $11.
You buy 1 pencil and 2 notebooks for $7.
Find the cost of one pencil.
$2
What type of line is used when graphing ≤ or ≥ ?
Solid Line
What does the solution to a system represent on a graph?
The point where the two lines intersect
Solve:
-2x + y = - 1
4x + 3y = 5
(1, 1)
Solve:
2x + 3y = 13
4x − 5y = 1
(-1, 5)
A gym charges a $20 membership fee plus $5 per visit.
Another gym charges $10 membership plus $7 per visit.
After how many visits will the cost be the same?
5 visits
What type of line is used when graphing < or > ?
Dotted Line
Without graphing, determine the type of solution:
y = 3x + 2
6x - 2y = -4
Infinitely Many Solutions
Solve:
2x + y = 8
3x + y = 2
(6, -4)
Solve:
3x + 4y = 18
5x − 6y = 2
(2, 3)
Two numbers add up to 42.
One number is 6 more than three times the other.
Find the two numbers.
9 and 33
Name the solution to a system of inequalities.
The overlapping shaded region.