1. 1.7 - Exploring Linear SystemsB C
2x + 3y = -4
-4x – 3y = -1
2y = 6 – 3x
6x – 5 = -4y
x – y = 5
3x = y
How many solutions can a linear system have?
How can you predict the number of solutions without solving the system? A B C
Linear System
2x + 3y = -4
-4x – 3y = -1
2y = 6 – 3x
6x – 5 = -4y
x – y = 5
3x = y
Number of Solutions ?

2. Case A One point of intersection, so 1 solution.
2x + 3y = -4
-4x – 3y = -1
One point of intersection, so 1 solution.
The coefficients and constants are not multiplied by the same amount.

3. Case B No points of intersection, so no solutions.
2y = 6 – 3x
6x – 5 = -4y
Case B
No points of intersection, so no solutions.
The coefficients are multiplied by the same amount, but the constants are not.

4. C
x – y = 5
3x = y
Case C
2 lines overlap, so every point in one line intersects with the other line.
Infinite number of solutions
Coefficients and constants are multiplied by the same amount.

5. In Summary…
A linear system can have no solution, one solution, or an infinite number of solutions.