Systems Review

Systems Review

What is the solution to a system?

The point where your two lines intersect is the solution. It has an x AND y

(x,y)

What methods did we use to solve?

• Graphing

• Substitution

• Elimination

Multiple Select

When do we use graphing method?

• Both equations are in slope-intercept form

• Both equations are in the form x+y=#

• Both equations are solved for one variable

With graphing, we know....

• Lines intersect- solution is: (x,y)

• Lines are parallel- NO SOLUTION

• Lines are same: INFINITELY MANY SOLUTIONS

Multiple Choice

What is the solution?

• (2,0)

• (1,1)

• (1,-1)

• (0,1)

Multiple Choice

When do we use substitution method?

• When both equations are in y=mx+b from

• When ONE equation is solved for one variable (either x= or y=)

• When BOTH equations are solved for x

With substitution:

• If #=# is a true statement, then INFINITELY MANY SOLUTIONS (example: 5=5)

• If #=# is a false statement, then NO SOLUTION (example: -7=2)

Multiple Choice

What is the first step to solve the system by substitution?

3x+4y=-11

y=2x

• 3x+4y=2x

• 3(2y)+4y=-11

• y=2(3x+4y)

• 3x+4(2x)=-11

DON'T FORGET!!!!

• Your solution is a pair (x,y), not just x or y

• Always plug in the value you found for x or y into EITHER equation to find the other variable value.

• Example, x=3-y and 3y+x=5. If y=1, what is x?

Multiple Choice

When do we use Elimination?

• When both equations are in slope-intercept

• When one equation is solved for one variable

• When the equations are lined up (stacked) with like terms vertically

Elimination

• Line up equations (rearrange if need be)

• Pick a variable (either x or y) to eliminate or cancel

• Make coefficients are SAME number, OPPOSITE sign. Example: 2x and -2x

Multiple Choice

Which variable will be eliminated?

4x+8y=20

-4x+2y=30

• y

• x

• neither

• 4

Multiple Choice

Which number would we multiply our second equation by to eliminate a variable?

2x+3y=6

5x-y=13

• -3

• -1

• 1

• 3

Multiple Choice

Which is the best method to solve?

2x-3y=-1

y=x-1

• Graphing

• Substitution

• Elimination

Multiple Choice

Which is the best method to solve?

-6x-2y=12

6x+8y=24

• Graphing

• Substitution

• Elimination

Multiple Choice

Which is the best method to solve?

y=2x+7

y=-3x-15

• Graphing

• Substitution

• Elimination

Go to link in and Watch from: 6:20-9:50

https://www.youtube.com/watch?v=Tkrqrfkznoo

Poll

How do you feel about solving systems of equations?

• Great!

• Pretty good, still need pracice

• Not good

• :(