Solving Systems Algebraically

Solving Systems Algebraically

Today we will

• Review what it means to solve a system

• Review how to solve by graphing by hand and by computer

• Introduce solving by system

Open Ended

What does it mean to solve a system of equations?

Multiple Choice

On your paper, sketch a graph of the following system and solve:

 $y=-x-1$   $y=-4x+2\ \ \ \ \ \ \$  

• (-1, -2)

• (1, -2)

• (1, 4)

• (-2, 1) 

Multiple Choice

Open a new tab or window and go to Desmos.com > click "graphing calculator". Use Desmos to solve the following system:

 $y=8x-4$ 
 $y=x+3$    

• (1, -1)

• (1, 4)

• (4, 1)

• (-1, 4) 

Sometimes, Graphing is inconvenient

• No computer

• not in "graphing friendly form"

• hate graphing

• etc.

Solving by Substitution

• The length of a rectangle is 2 cm more than 3 times its width.

• If the perimeter of the rectangle is 28 cm, find its dimensions

The length of a rectangle is 2 cm more than 3 times its width.

• L = 3w + 2

The perimeter of the rectangle is 28 cm

• 2L + 2w = 28

Create the system

• L = 3w + 2

• 2L+ 2w = 28

• What do you notice? What do you wonder?

Poll

What should we do?

 $L=\ 3w+2$   

 $2L+2w=28$  

• Move to slope intercept and graph

• Use desmos to do the work for me

• I bet there is a better way.

Substitution

2L + 2w = 28 and L = 3w + 2

so

2(3w+2) + 2w = 28

(6w+4) + 2w = 28

8w +4 = 28

8w = 24

w = 3

Now that we have w....

• w = 3 and

• L = 3w + 2

• L = 3(3) + 2

• L = 11

• Solution (11, 3)

Multiple Choice

Solve

 $4x\ -\ y=-22$ 
 $y=x+10$  

• (-4, 8)

• (2, 8) 

• (4, 8)

• (-4, 6)

Multiple Choice

Solve: 
 $y=2x-14$ 
 $y=-2x+14$  

• (0, 7)

• (7, 0)

• (0, -7)

• (0, 1)

Open Ended

What questions do you still have about solving with substitution?