Linear Equations Applications Problems with Systems of Equations

Solve the system using any method. 
−4x − 4y = 0
4x + 4y = 0 

• (−6, −4) 

• Infinite number of solutions  

• No solutions

• (6, 4) 

Solve by graphing:
y=5x+3

y=-2x-4

• (2,-1)

• (-1,-2)

• (1,-2)

• (-2,-1)

How can you tell if a point is a solution to a system?

• It makes the first equation true.

• The (x,y) coordinates satisfy both equations

• It makes logical sense

• It makes neither equation negative

When you graph the exact same equation twice,

• you will have no solution. 

• you will have one solution.

• you will have infinite solutions. 

• you will graph a giraffe. 

Solve the following system of equations using the elimination method.

• infinite solutions

• (0, -2)

• no solutions

• (0, 2)

What category does this belong in?

Common real-world applications: prices and quantities, speed and distance, constant change over time.

• Linear functions and equations

• Systems of equations and inequalities

• Quadratic functions and equations

• Exponential functions and equations

What category does this belong in?

• Linear functions and equations

• Systems of equations and inequalities

• Quadratic functions and equations

• Exponential functions and equations

What category does this belong in?

• Linear functions and equations

• Systems of equations and inequalities

• Quadratic functions and equations

• Exponential functions and equations

What category does this belong in?

There are three methods for solving: Graphing Method, Substitution Method, and Elimination Method

• Linear functions and equations

• Systems of equations and inequalities

• Quadratic functions and equations

• Exponential functions and equations

What category does this belong in?

• Linear functions and equations

• Systems of equations and inequalities

• Quadratic functions and equations

• Exponential functions and equations