Solving Systems

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? 

2x+y=4

14x+7y=28

Infinitely Many Solutions

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? 

-4x+10y=6

2x-5y=3

No solution

Selecting Method

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)