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Solving Equations
How Many Solutions?
Solving Systems by Graphing
Solving Systems by Substitution
Mixed
100
Solve for x: 3x + 12 = 33

x = 7

100

How many solutions does this equation have?

2x  + 3 = 3 + 2x

Infinite Solutions

100
How can I find a solution to a system by graphing?

Graphing the lines and seeing where they cross.

100

Solve this system of equations:

y = 5 

y = 3x - 7

(4, 5)

100

Create an system of equation for these: 

Jada bank offers an incentive for getting a savings account by giving new accounts $26 and Jada plans to save $7 each week after she opens her account.Andre's bank offers a similar incentive of $50 for new accounts and he plans to save $5 each week after he opens the account.

y = 7x + 26

y = 5x + 50

200

Solve for x:

2 (3x + 1) = 32

x = 5

200

How many solutions does this equation have?

7(x - 4) = 4x + 5 

One Solution

200

How would you graph this line?

y = 2x - 5

Start at -5.  Move by a slope of 2 (up 2, right 1)

200

y = 3x

y = 5x -2

(-1, -3)
200

Does this have a solution of (5, 2)

y = x - 3

y= -x + 3

NO.

300

x + 3 - 2x = 7 - 2x

x = 4

300

How many solutions does this equation have?

-6x = -6x - 1

NO Solution

300

What does a graph look like with no solutions?

Parallel Lines 

300
x = 6

y = 4x + 2

(6, 27)

300

When will Jada and Andre have the same amount money? How much money will they have? 

Jada bank offers an incentive for getting a savings account by giving new accounts $26 and Jada plans to save $7 each week after she opens her account.Andre's bank offers a similar incentive of $50 for new accounts and he plans to save $5 each week after he opens the account.

12 weeks and $110

400

Solve for x:

3(2x - 1) - 10 = 8 + 5x

x = 21

400

How many solutions does this equation have?

2x + 3 = 2x + 5

No Solution

400

What does a graph look like if there is infinitely many solutions?

Two lines in the same location (on top of each other)

400

y = x - 3

y = -2x + 12

(5, 2)

400

Who has more money after 4 weeks of saving?

Jada bank offers an incentive for getting a savings account by giving new accounts $26 and Jada plans to save $7 each week after she opens her account.Andre's bank offers a similar incentive of $50 for new accounts and he plans to save $5 each week after he opens the account.

Andre

500

-2(3x +5) = 1/2 (-8x + 4)

x = -6

500

How many solutions does this equation have?

4 (x - 2) = 4x - 8

Infinite Solutions

500

graph these two equations:

y=2x+1

y=−x+7

Cross at (2, 5)

500

y = 2x + 1

2x + 2y = 14

(2, 5) 

500

Is (4,3) a solution to this system?

y = x - 1

2x - y = 5

Yes