Checking Solutions to a System

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

• They are parallel.

• They are the same line.

• They intersect.

How many solutions does this system of equations have?

• One

• None

• Infinitely many

• Two

Which is the solution to this system?

x - y = 6

y = 2x - 5

• (1, 3)

• (-1, 3)

• (-1, -7)

• (1, -7)

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

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

• No; it satisfies the first equation, but not the second.

• No; it satisfies the second equation, but not the first.

• No, it fails to satisfy either equation.

If a system of equations has no solution, what does the graph look like?

• Intersecting lines

• Parallel lines

• A single line

• Curved lines

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

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

• yes

• no

What is the solution to this system of equations?

• (2,1)

• No Solution

• (-2, -1)

• (0, -3)

What is the solution to this system of equations?

• (2,2)

• (0,3)

• (0,0)

• No Solution

What is the solution to this system of equations?

• (0,-2)

• No Solution

• (3,-1)

• (4,0)