Solving Systems of Equations

Solving Systems of Equations

Graphing, Substitution, and Elimination

vocabulary

• consistent - at least one solution

• inconsistent - no solution

• independent - one solution

• dependent - infinitely many solutions

Multiple Choice

This is an example of a system of linear equations that are

• consistent and independent

• consistent

• inconsistent and dependent

• consistent and dependent

Multiple Choice

This is an example of a system of linear equations that are

• consistent and independent

• inconsistent

• inconsistent and independent

• inconsistent and dependent

Multiple Choice

This is an example of a system of linear equations that are

• consistent and independent

• inconsistent

• inconsistent and independent

• consistent and dependent

Multiple Choice

A consistent system that has exactly one solution

• inconsistent

• consistent

• dependent

• independent

Multiple Choice

A consistent system that has infinitely many solutions is

• dependent

• consistent

• independent

• inconsistent

Multiple Choice

Inconsistent system is a system of equations that has

• one solution

• two solutions

• infinitely many solutions.

• has no solution

Multiple Choice

A system of equations that has a least one solution is

• Consistent

• inconsistent

• dependent

• independent

Solving Systems of Equations by Graphing

• Make sure both equations are in slope intercept form

• Graph both equations on the coordinate plane

• Find the point of intersection

Multiple Choice

What is the solution to a systems of equations? 

• The point or points where they intersect
• What the lines have in common
• Either a single point, infinite number of points or no points
• ALL OF THE ABOVE 

Multiple Choice

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

• intersecting lines
• parallel lines
• skew lines
• intersecting lines

Multiple Choice

The solution to this system of equations is:

• (4, 3)
• (3, 4)
• (-4, 3)
• No solution

Multiple Choice

These two lines intersect at _____.

• (4, -2)
• (4, 2)
• (-2, 4) 
• No solution

Multiple Choice

7x + y = -20
y = 3x + 10

• (-3, 1)
• (-1, -3)
• (-3,-7)
• (-1,7)

Multiple Choice

x + 2y = 2
x = -4y + 2

• (-3, 0)
• (0, 2)
• (-3, -2)
• (2, 0)

Multiple Choice

Solve this system of equations. 
y = 2x + 1
y = 4x - 1

• (1,3)
• (-1,-3)
• (-1,3)
• (3,1)

Multiple Choice

Solve the system by substitution.
 
5x + 4y= −14
y =  −7x  −  15 

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

Multiple Choice

y = -2x + 18
y = 8

• (5, 8)
• (-5, 8)
• (2, 8)
• (-2, 8)

Multiple Choice

Solve by elimination:
3x + 7y = 23
-3x - 7y = -17

• No solution
• Infinite number of solutions
• (-3,3)
• (3,3)

Multiple Choice

Solve by elimination:
4x + 4y = 4
   3x + 4y =10

• (7,-6)
• (-6,7)
• (6,7)
• (7,6)

Multiple Choice

Solve by elimination 
  2x + 9y = -7
6x - 3y = 9 

• (-1, -1) 
• (2,-1)
• (1,1)
• (1,-1)

Multiple Choice

 Solve using elimination.
 7x + 2y = 24
  8x + 2y = 30

• (6,-9)
• (-9,6)
• No solution
• Infinite number of solutions

Multiple Choice

Solve using Elimination. 
 4x + 8y =  20
-4x + 2y = -30

• (-7,1)
• (2,-5)
• (-2,5)
• (7,-1)