Systems Special Solutions by Inspection

Jane is practicing solving systems of equations by inspection. She thinks that y = 5/6x + 2 and y = 5/6x – 2 would have exactly one solution. Is she correct? Why or why not?

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

• Parallel lines

• the same line 

• Intersecting lines

y = 3x + 2 and y = -3x + 2

• no solutions

• 1 solution

• infinitely many solutions

y = -x + 2 and y = -x + 2

• 1 solution

• no solutions

• infinitely many solutions

y = 5x - 2 and y = 2x - 5

• no solutions

• 1 solution

• infinitely many solutions

y = 3x + 5 and y = 5 + 3x

• infinitely many solutions

• 1 solution

• no solution

y = -3x - 2 and 4y = 12x - 8

• no solutions

• 1 solution

• infinitely many solutions

y = -7x + 2 and 2y = -14x + 6

• no solution

• 1 solution

• infinitely many solutions

Is the ordered pair (2,1) a solution to the system?

• Yes

• No

Is the ordered pair (-2, 1) a solution to the system of equations?

• Yes

• No