Proving Solutions to Systems

What is the solution to this system of equations?

• (2,1)

• No Solution

• (-2, -1)

• (0, -3)

How many solutions?

• One Solution

• No solution

• Infinitely Many Solutions

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

• Yes

• No

How can you tell if a point is a solution to a system?

• It makes the first equation true.

• The (x,y) coordinates satisfy both equations

• It makes logical sense

• It makes neither equation negative

Solve the system.

• (1, 2, -2)

• (1, -3, -2)

• (-1, 3, 2)

• No Solution

Solve the system.

• (3, -2, 4)

• (2, -3, 1)

• (-3, 2, -1)

• Infinitely many solutions

Solve the system.

• (2, -2, 3)

• (2, 1, 4)

• (-2, 2, -3)

• No Solution

Solve the system. 

• (5, -6, 3)

• (2, 3, -1)

• (-4, 2, 5)

• No Solution

How many solutions does the system of equations on the graph have?

• One Solution

• No Solution

• Many Solutions

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

• YES

• NO