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

What would you need to do first to solve this system by substitution 

2x=16y+8

3x+4y=-10

Divide the top equation by 2 to get x by itself

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

When is the elimination method convenient for solving a system of equations? 

When there are equal or opposite coefficients for one of the variables. 

200

What if the variables have the same number and the same sign, what do you need to do first in order to use elimination? 

For example 

5x+4y=20

6x+4y=1

Multiply one equation by -1

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

When is graphing the best method for solving a system of equations? 

When both equations are in slope intercept form or can easily be turned into slope intercept form. 

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 would this 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.