Solving System of Equation Mixed Methods

What is the solution?

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

Give the solution to the system.

• (3,1)
• (1,3)
• (-1,3)
• (1, -3)

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

• Parallel lines
• the same line 
• Intersecting lines

Based on the equations for each line, determine how many solutions the system would have.

y = 2x + 3

y = -4x + 3

• Infinite Number of Solutions

• No Solution

• One Solution

Based on the equations for each line, determine how many solutions the system would have.

y = -3x + 2

y = -3x + 2

• Infinite Number of Solutions

• No Solution

• One Solution

What is the best method to use?

−4x − 2y = −12

4x + 8y = −24

• Graphing

• Substitution because a variable is defined

• Elimination because the equations are in standard form.

What variable do you eliminate?

4x + 8y = 20

−4x + 2y = −30

• X because they have opposite signs

• Y because they have opposite signs

What is the proper set up to solve the equation?

-7x -2y= -13

x = 2y+11

• -7(11) -2y = -13

• -7(2y +11)-2y = -13

• -7x -2(11) =-13

• -7x - 2(2y+11)= -13

When will we get "no solutions" from a system of equations?

• The two lines cross once

• The two lines are the same and overlap

• The two lines are parallel and never touch

• The two lines cross at 2 points