Solution to Systems of Equations

Solve the system using your calculator.

You and your friend are buying throw blankets with your names embroidered on them. The cost of the throw blanket is x dollars and the cost of each embroidered letter is y dollars. Your name has 6 letters and the total cost is $29. Your friend's name has 3 letters and the total cost is $24.50. Which system can you use to solve this problem?

What is the type of solution to the system of equations?
y = 1/4x - 3
y = 2/8x - 3

• one solution

• no solution

• infinitely many solutions

What is the type of solution to the system of equations?
y = -x -6
y = 2x + 6

• one solution

• no solution

• infinitely many solutions

• none of the above

What is the type of solution to the system of equations?
y = -2x - 7
y = -2x + 8

• one solution

• no solution

• infinitely many solutions

• Infinite solutions

• No solution

• One Solution

• Two Solutions

A system with one solution has...

• Same Slope; Same y-Intercept

• Same Slope; Different y-Intercept

• Different Slopes

• Not Possible

A system with Infinite Solutions has...

• Different Slopes

• Same Slopes; Same y-Intercepts

• Same Slopes; Different y-Intercepts

• all vertical lines

• y =  $\frac{2}{5}$  x - 9;

•  $\frac{2}{5}$  x + 3

• y = 5x + 2

• 2x + 5y = 9

How many solutions does the system have?

y = 2x + 3

y = 3x + 4

• Exactly one solution

• No solutions

• Infinitely many solutions