Systems with No Solution or
Infinitely Many Solutions
September 15, 2014
Pg. 21 in Notes
Warm-Up (pg. 20)
• Solve the following system of equations using
the elimination method.
• 7x + 4y = 2
• 9x – 4y = 30
Questions on Friday’s Assignment?
No Solution/Infinitely Many Solutions
• Title: page 21
Essential Question
• How do you know if a system has one
solution, no solution, or infinitely many
solutions?
Systems with One Solution
• Solution will be an ordered pair.
Systems with No Solution (NS)
• When solving, statement is untrue.
• Example:
y = 3x + 1
6x – 2y = 5
Let’s use substitution:
6x – 2(3x + 1) = 5
6x – 6x – 2 = 5
-2 = 5
The variable canceled and this
statement is untrue, so this
system has no solution.
Systems with Infinitely Many Solutions
• When solving, statement is always true.
• Example:
2x + 3y = 6
-4x – 6y = -12
Let’s use elimination:
8x + 12y = 24
-8x – 12y = -24
0=0
Each term canceled and this
statement is always true, so this
system has infinitely many
solutions.
Practice – Determine whether each of the following
systems of equations has one solution, no solution, or
infinitely many solutions.
1. 7x + y = 13
28x + 4y = -12
5. 24x – 27y = 42
-9y + 8x = 14
2. 2x – 3y = -15
3y – 2x = 15
6. 3/2 x + 9 = y
4y – 6x = 36
3. 8y – 24x = 64
9y + 45x = 72
7. 7y + 42x = 56
25x – 5y = 100
4. 2x + 2y = -10
4x – 4y = -16
8. 3y = 2x
-4x + 6y = 3
Reflection
1. If no solution means there is no ordered pair
that will make both equations true, what will
that look like when graphed?
2. If infinitely many solutions means any
ordered pair that makes one equation true
will make the other equation true as well,
what will that look like when graphed?