Systems of Equations

What is the solution to this system?

• (1, -1)
• (-1, 1)
• (0, -2)
• (2, 0)

How many solutions will this system have? 

• No solution
• One Solution
• Two Solutions

• 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

Solve this system by substitution.

• (1, -4)

• (1, 4)

• (-4, -7)

• (-7, -4)

Solve for x and y
2x − 3y = −1
 y = x − 1

• (-2,-3)
• (0,-1)
• (3,4)
• (4,3)

Solve by elimination:
4x + 9y = 28
-4x - y = -28

• (-7,0)
• (6,0)
• (-6,0)
• (7,0)

Solve by elimination:

3x + 7y = 23

-3x - 7y = -17

• No solution

• (0, 3)

• (-3,3)

• (3,3)

What is the best method to use?

2x − 3y = −1

y =x − 1

• Graphing

• Substitution because a variable is isolated

• Elimination because the equations are in standard form.

What is the best method to use?

−4x − 2y = −12

4x + 8y = −24

• Graphing

• Substitution because a variable is isolated

• Elimination because the equations are in standard form.

Nancy went to the grocery story. On Monday she purchased 4 apples and 6 bananas for a total of $13. On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50. Which system of equations represents the situation?

• 4x + 6y = 3

  13.5x - 13y = 6

• x + y = 4

  x - y = 6

• 4x + 6y = 13

  3x + 7y = 13.5

• 4x - 6y = 13

  3x - 7y = 13.5