Solving Systems of Equations by Graphing, Substitution, or Elimination

Solve the system by elimination. 
−4x − 4y = 0
4x + 4y = 0 

• (−6, −4) 

• Infinite number of solutions  

• (−6, 10) 

• (6, 4) 

Solve this system by substitution.

• (1, -4)

• (1, 4)

• (-4, -7)

• (-7, -4)

Solve for x and solve for y
3x  - 3y = 33
6x - 3y = 57

• (8,-3)

• (-3,8)

• (10,1)

• (10,-1)

2 or more linear equations with the same set of variables

• System

• System of Equations

• Linear Equations

• Quadratic Equations

a solution to a system that results in one x value and one y value that will satisfy both equations 

• No Solution

• One Solution

• Infinite Solutions

• Beyond Solutions

a solution to a system that results in an unlimited amount of x values and an unlimited amount of y values that will satisfy both equations

• No Solution

• One Solution

• Infinite Solutions

• Beyond Solutions

a solution to a system of equations that results in no x or y value that will satisfy both equations

• No Solution

• One Solution

• Infinite Solutions

• Beyond Solutions

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

• Infinitely Many Solutions
• No Solution

The solution (x, y) to a system of equations is the point where they...? 

• Run off the graph

• Don't touch

• Intersect

• Exist