How Many Solutions Equations and Systems

Solve the following System of Equations using the Substitution Method:

• (2, -8)

• (1, -11)

• no solution

• (-12, -40)

How many solutions does this system of equations have?

• One Solution

• No solution

• Infinitely Many Solutions

• Two Solutions

How many solutions will this system have?

• One

• Two

• No Solution

• Infinitely Many Solutions

If a system of linear equations has one solution, what does this mean about the two lines?

• Parallel lines

• the same line

• Intersecting lines

What is the Solution to this system?

• (2,-2)

• (-2,2)

• All Real Numbers

• No Solution

What is the solution to the system?

• (3, -1)

• (2, -6)

• No Solution 

• (6, -2)

Solve by inspection

y= ¾ x + 5

y= ¾ x + 2

• No Solution

• One Solution

• Infinitely Many Solutions

solve by inspection

y= ¾ x + 5

y= -¾ x + 5

• No Solution

• One Solution

• Infinitely Many Solutions

• No Solution

• One Solution

• Infinitely Many Solutions

Which is a true statement about the system of equations graphed below?

• The system of equations does not have a solution because

  the lines do not intersect.

• The system of equations has one solution, although it is not

  visible on the graph.

• The system of equations has an infinite number of solutions.

• None of the statements above are true.