Solving Systems

By Graphing

100

What do you need to identify from each equation before solving by graphing?

What the slope is (m) and what the y-intercept is (b).

200

What is m and b in each of the following equations? 

y=3x+2 

y=-1/2x-7

M=3 b=2 M=-1/2 b=-7

300

What is the solution to the following system of equations? (You have to graph them) 

y=x-3 

y=-x-1

(1,-2)

400

What is the solution to the following system of equations? (You have to graph them) 

y=-2x-1 

y=x+5

(-2,3)

500

What is the solution to the following system of equations? (You have to graph them) 

y=-x+6 

y=x

(3,3)

By Substitution

100

How many steps are there total to solve systems by substitution?

3

200

Do we have to complete step 1 if the system is as follows? 

x=2y-4 

x=-8y+16

No, 1 or more equations are solved for a variable.

300

What is the solution to the following system? 

y=x+3

 y=2x+5

(-2,1)

400

What is the solution to the following system? 

x=2y-4 

x+8y=16

(0,2)

500

What is the solution to the following system? 

x=y-8 

-x-y=0

(-4,4)

By Elimination

100

How many total steps are there when you solve systems by elimination?

6

200

What do you need one of your variables to have so you can eliminate? What do they look like?

Opposite coefficients. Same number in front of x or y terms with one positive and one negative.

300

Solve: 

 3x-y=-2 

-2x+y=3

(1,5)

400

Solve:

 x +2y = 5 

3x+2y = 17

(6, -1/2)

500

What is the solution to the following system? 

x-y=-3 

5x+3y=1

(-1,2)

SelectingMethod

100

What should both of your equations look like when you choose to solve by graphing? What format should they be in?

y=mx+b Slope intercept form Both solved for y

200

What is one reason that you would choose to solve by substitution?

Both equations are solved for a variable. 1 equation is solved for a variable. A variable in either equation has a coefficient of 1 or -1.

300

What method would you use if you had the following system of equations? 

-x+y=5

X-5y=-9

Elimination

400

What method would you use if you had the following system of equations?

 y=x+5 

4x+y=20

Substitution

500

What is the solution? Pick a method and solve. 

y=x+5 

y=2x

(5,10)

Systems info

100

How many equations are in a system of equations?

2 or more

200

What should your answer be written as when solving systems?

An ordered pair.

300

How do you check your answer when solving systems of equations?

You plug the ordered pair back into both equations and see if you get the same number on both sides of the equals sign for both equations.

400

It is possible to have no solution to a system of linear equations. When solving by graphing what you that look like?

Two lines that are parallel and do not intersect.

500

It is possible to have infinitely many solutions to a system of linear equations? When solving by graphing what would that look like? What would the equations look like?

Yes. The same line. They would have the same slope and y-intercept.