Algebra 1 10 Feb 2012WARM UP- THINK- 2 minutes silently PAIR- chat with a partner

1) Which values make both equations true? W + M = 25 W = M + 5a) W = 20, M = 5 b) W = 10, M = 15 c) W = 15, M = 10Explain how you know you are correct

2) Solve 10 – x = 20 showing all steps

objectivesStudents will solve systems of equations using algebra.Students will watch a video and participate in whole class discussion.

Homework due TODAYHomework due TODAY

pg. 285: 1- 4pg. 285: 1- 4Homework due TUESDAYHomework due TUESDAY

your handout- distributive propertyyour handout- distributive property

Systems of equations from word problems 1) define variables

2) write equations 3) solve for y if needed 4) substitute the equivalent expression 5) combine like terms 6) solve for the first variable 7) PLUG your answer IN one equation to FIND THE SECOND VARIABLE!!! 8) PLUG both values in the 2nd equation to check!

Systems using substitution

Consider the system y = 30 – 2x y = 40 – 4xThe SOLUTION is the (x, y) point where both lines intersect. We can sometimes see the solution in a table: x 0 1 2 3 4 5

y1 30 28 26 24 22 20

y2 40 36 32 28 24 20

On a graph, the solution iswhere the two lines INTERSECT

The POINT represents the values for X AND Y that make BOTH EQUATIONS TRUE!

1 2 3 4 5 6 7 8 9 days

5

10

15

20

25

30

35

40

45

50apples

SOLUTION!!(x, y) = (x,y) x = x y = y

Algebraically….If we have two equations, in y = mx + b form, or y= form, we can find the solution that makes both equations true by SUBSTITUTION!!Example: y = 3 y = 2x + 10 In the solution, both x = x and y = y. SO, we can write let y = y

3 = 2x + 10NOW SOLVE FOR X……..Then substitute back in to check (we already know “Y”)

Practice….

SOLVE THE SYSTEMS FOR X AND Y X AND Y then CHECK!1)Y = 5, Y = 20 – 5x2)Y = 10, y = 2 + 2x3)Y = 100, y = 10 + 6x4)Y = 5x, y = 14 – 2x5)Y = 10x, y = 50 -15x

REMEMBER– your solution is x= AND y= don’t forget to CHECK

EXAMPLE: y = 3x, x + y = 16 HOW CAN WE SOLVE by substitution???WE STILL WANT VALUES THAT MAKE BOTH EQUATIONS TRUE….we still want y = y… so x + y = 16 x + ??? = 16

What if one equation is NOT y=?

X + 3x = 16

SOLVE for x, then substitute back to solve for y ---don’t forget to CHECK!

handout

Start with 2, 4 and 6….. Got it? Now do 5…. What do you think? Move on to 3, 7, 8 and 9!!

Remember– solve for FIRST variable plug it in to an equation to find SECOND variable plug both values in to the other equation to check!!

Khan Academy

Watch video- Solving systems graphically Solving systems using substitution

http://www.khanacademy.org/video/solving-linear-systems-by-substitution?topic=algebra-worked-examples-2

Work on your substitution handout.

Exit QuizSet up and solve the system of equationsShow all your steps clearly and concisely.

Make sure you CHECK your solution.

Do your work on your handout.