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Concepts

100

What is a system of linear equations?

A set of two or more lines.

200

What is the "solution" to a system?

The point of intersection.

300

Juppy Flibbets decides to answer a systems problem with "the answer is 4." How do I know he's wrong?

Because the answer will always be a point in the form (x,y).

400

What are the SIX ways we have learned to solve equations?

1. Graph by hand

2. Graph on calculator

3. Substitute

4. Elimination Subtraction

5. Elimination Addition

6. Elimination Multiplication

500

In the system

2y=5x+1

-3y=5x-2

The second equation looks hard. How can I make it easier?

Change the signs by multiplying by negative one.

How Many Solutions?

100

If two lines are parallel, how many solutions will there be?

0. Parallel lines never intersect, so they will never touch or have solutions.

200

If a line crosses another line, how many solutions will there be?

1, the point of intersection. This is what most of our lines look like in this class.

300

If two lines are right on top of each other, how many possible solutions are there?

Infinite. Every point on the lines is on both lines.

400

y=3x+4

y=3x- 2

How many solutions does this have?

0, because they are parallel. Look at their slopes.

500

How many solutions are there for this system: y=2x-1 y=3x+4

One. They are intersecting lines.

Solve (Easy)

100

How would you solve this problem:

y=2x+1

y=3x-4

You would use the graphing technique.

200

How would you solve this problem:

x=4

y=2x

What is substitution.

300

Solve this problem:

y=3x-1

x=2

(2,5)

400

How would you solve the following?

2x+3y=5

4x+3y=7

Elimination subtraction.

500

Solve the following: (hint: graph it)

x=2

y=4

(2,4)

Solve (Medium)

100

Solve:

2x+3y=5

4x+3y=7

(1,1)

200

Solve:

3x+2y=10

-3x+4y=20

What is (0,5)

300

Solve:

x+5y=7

3x+5y=11

(2,1)

400

y=3x+4

x+y=12

(2, 10)

500

Substitute:

y=2x+4 x=y-8

(4,12)

Solve (hard)

100

−6x + 5y = 1

6x + 4y = −10

(-1,-1)

200

Johnny Buckets buys 2 burritos and 3 sodas on one day, and it costs him $15. The next day, he buys 5 burritos, and 1 soda, and it costs him $31. How much is a burrito? A soda?

Burrito: $6

Soda: $1