Homework Systems of Equations

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

• Parallel lines

• the same line

• Intersecting lines

If a system of equations has infinitely many solutions, what does the graph look like? 

• intersecting lines

• parallel lines

• skew lines

• the same line (coinciding lines)

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

The graph of two linear equations is shown. What is the best estimate to the solution of the system of equations?

• (2, 1)

• (1, 2)

• (-4, 2)

• (4, 2)

The solution is:

• (4, 3)

• (3, 4)

• (-4, 3)

• No solution

• (-1, -4)
• (-1, -3)
• (-3, -1)
• (-4, -1)

• (-3, 0)
• (0, 3)
• (3, 0)
• (0, -3)

• (2, 0)
• (-2, 0)
• (0, 2)
• (0, -2)

Determine if (4, 1) is a solution for the system of equations. (Hint: Substitute x and y values into each equation)

y = -x + 5

y = 2x - 7

• yes

• no

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

• intersecting lines

• parallel lines

• skew lines

• the same line (coinciding lines)