Solving Systems of Equations Graphing Substitution Elimination

Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

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)

Identify which method for solving systems is being described by this fact:
If one equation is isolated like y = 2x or x = 7 - 4y then this method should be used.

• Graphing

• Substitution

• Elimination (linear combination)

When solving the system, if you get a result of something like 6 = 6 or -2 = -2 and the answer is:

• No Solution

• Infinitely Many Solutions

• Not possible

What is the solution to the system of equations? 
y = 3x - 8
y = 4 - x

• (3,1)

• (1,3)

• (-3,1)

• (3,-1)

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

• (−6, −4) 

• Infinite number of solutions  

• (−6, 10) 

• (6, 4) 

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