Nature of Solutions of Systems of Equations

x = x

• No Solution

• One Solution

• Infinite Solutions

• Beyond Solutions

What point is a solution to the system of equations below?

3x + 2y = 16

7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

Will the solution (-3, -7) make the following system of equations a true statement? 
y = 4x + 5
y = x – 4

• YES

• NO

Determine if (4, 1) is a solution for the system of equations.
y = -x + 5
y = 2x - 7

• yes

• no

Is the point (2, -1) a solution to the systems of equations below?

• Yes

• No

How many solutions?

• 1 Solution

• 2 Solutions

• No solutions

• Infinite solutions

Why will these graphs never cross?

• They have the same y-intercept.

• They have the same slope.

• They are both lines.

• They are both positive slopes.

How many solutions?

• 1 solution

• 2 solutions

• No solutions

• Infinite Solutions

Is (4, 5) a solution to the system of equations?
4x+y=21
-3x-6y=10

• Yes, it is a solution to the system of equations

• No, it only satisfies the first equation, and fails to satisfy the second.

• No, it only satisfies the second equation, and fails to satisfy the first.

• No, it fails to satisfy both equations

Is (-2,7) a solution to the system of equations?
y=4x+15
-3x+5y=41

• Yes, it is a solution to the system of equations

• No, it only satisfies the first equation, and fails to satisfy the second.

• No, it only satisfies the second equation, and fails to satisfy the first.

• No, it fails to satisfy both equations