Algebra Warm up:

pg. 330 # 36 to 43

7.2 Substitution Method pg. 326 to 330

THIS method helps you to find the EXACT answer without graphing!!!!

REMEMBER:

You are solving systems of equations!( 2 equations with 2 variables at the same time)( the (x, y) are the SAME in both equations)

The Substitution method-- allows you to get that answer without graphing anything!

-just remember how to combine like terms and solve for a variable!

Systems Equations Video.mov

Solve the system of equations using the substitution method...

8x + 2y = 19

x = 3

8 (3) + 2y = 19

24 + 2y = 19-24 -24

2y = -5 2 2

y = -2.5

Final answer (3, -2.5)

System of equationsMake sure ONE equation is solved for ONE of the variables (does not matter which one)

Substitute that "answer" into the corresponding variable in the OTHER equation.

Solve like any other problem.At this point THE OTHER VARIABLE is what you are solving for.

Form answer into coordinate pair.

Try this one...

10x + 2y = 10

y = -10

What happens when it is a little more complicated????

Solve by substitution method.

15x - 5y = 30

y = 2x + 3

15x - 5 (2x + 3) = 30

15x -10x -15 =30

5x -15 = 30 +15 +15

5x = 45 5 5

x = 9

THEN take that answer x =9and substitute it BACK into one of the ORIGINAL equations

y = 2 (9) + 3

y = 21

Final answer (9, 21)

Substitute

Distributive property

SimplifyCombine like terms

ONE Answer

DivideFinal Answer (9, 21)

Try these.....

10x + 2y = 10

y = 3x - 3

-3x + 2y = 31

x = 0.5y +6

How do you know that your answers are correct?

SOLVE both equations and see if they are TRUE.

Is (2,8) a solution to this system of equations?

y = x + 33x + y = 11

Sometimes you have to do some rearranging first BEFORE you substitute and solve!

3x + y = 45x - 7y = 11

Are either of these READY for substitution?

So pick one (does not matter which BUT to make your life easier--pick the one where one of the variables DOES NOT have a coefficient)

3x + y = 4-3x -3x

y = -3x + 4

Can't combine becasue not like terms

Now you have one equation that is solved for a variable.........

Now the problem becomes......

y = -3x + 45x -7y = 11 So now you can use the substitution method!

Try this one....

6x - 2y = 11x + 3y = 4

So so far you have learned 2 Methods to solving systems of equations.

Graphing AND Substitution

How do you know which one to use if they don't care which method you use?

When would graphing work better?

When would substitution work better?

So try pg. 329 # 4-7

DON'T forget--answer in form of coordinate pair!