Systems of Equations

Systems of Equations

Multiple Choice

Ethan wins ? boxing matches every day. The graph represents the number of matches he has won over x days.

• Ethan wins 1 matches per day

• Ethan wins 2 matches per day

• Ethan wins 6 matches per day

• Ethan wins 10 matches per day

Multiple Choice

When will Ethan and Israel have the same number of wins?

• After 1 day

• After 5 days

• After 6 days

• After 10 days

The solution to a system of equation is a coordinate point that makes both equations true.

The point (1, 6) is where the two lines on the last slide intersected.

Ethan's Wins: y=6x when we plug in (1,6),

6=6(1) is true.

Multiple Choice

Plug in the same point (1,6) into the other equation for Israel's wins: y=1x+5.

• 1 = 1(6) + 5

• 6 = 1(1) + 5

To find the solution of two lines on a graph, you just need to find the point where they intersect.

Multiple Choice

What is the solution?

• (6, 3)
• (3, 6)
• (-6, 3)
• No solution

Multiple Choice

^{What is the solution?} 

• 1
• -2
• (1, 2)
• (1, -1)

Multiple Choice

Give the solution to the system.

• (3,1)
• (1,3)
• (-1,3)
• (1, -3)

Multiple Choice

What is the solution?

• (1, -1)

• (-1, 1)

• (0, -2)

• (0, 1)

Open Ended

The lines represent the amount of money Noah and Michael each have left on each of their gift cards.

What does the intersection point mean? (Include weeks and $ in your answer).

Poll

How well do you understand how to find the solution of two lines on a graph?

• I can explain it to others.

• I can usually get the right answer but I can't explain it.

• I kind of get it.

• I am confused.