2 Equations with 2 Unknowns Created by Daniel Seiltz Click Me
to Begin!
Slide 2
Navigation At any point in the instruction click here to go
back to the home page. Back one screen Forward one screen Once you
see this button Its Quiz Time!
Slide 3
Welcome Hey everybody! My name is Cal Culator but all my
friends call me Cal. I will be helping you throughout this
lesson.
Slide 4
Home Intro Addition Method Subtraction Method Home! Click on
the Buttons to Access any point in the Lesson. Note: Will not show
up until completion of both lessons
Slide 5
Intro Video
Slide 6
Review Can you remember back to Pre-Algebra when we studied
solving equations? This lesson will require you to use those same
skills in a new and exciting way.
Slide 7
Review Problem Solve the equation for y. 5 = 5y + 20x Advance
to see the worked out solution.
Slide 8
Worked Out Solution Starting Equation: 5 = 5y + 20x Subtract
20x from both sides: 5 20x = 5y + 20x 20x 5 20x = 5y 1 4x = y
Divide by 5: 1 4x = y
Slide 9
Lesson Preview In this lesson you will learn o To add two
equations in order to solve for the two variables in question. o To
subtract two equations in order to solve for the two variables. o
Distinguish between the two methods. o Choose which method to use
in different cases and situations. By the end of this lesson you
will have... o Learned each method and its basics. o Practiced each
method several time. o Taken a final quiz to assess your new
knowledge.
Slide 10
Lesson Preview Why are we learning this? o Adding and
Subtracting two equations to find two unknowns (variables) will be
used in every math class here and after all the way up through
linear algebra in college. o It is an essential skill that must be
mastered. Real World Application o I know some of you are asking
When are we ever going to need to do this in real life? o Next is a
real world application of the material you are about to learn.
Slide 11
Real World Application This problem is a real world application
of the knowledge to be learned. ''A total of $12,000 is invested in
two funds paying 9% and 11% simple interest. If the yearly interest
is $1,180, how much of the $12,000 is invested at each rate? By the
end of this lesson you will be able to solve these and similar
problems.
Slide 12
Overview The addition and subtraction methods are part of the
elimination method. The whole premise of this elimination method is
to o A) manipulate both equations to put all the variables on the
same side. o B) solve for a variable by eliminating the other
variable. o C) solve for the other variable by plugging back into
the original equation.
Slide 13
Addition Method Start with two equations with two variables
like these. x + 2y = 8 3x 2y = 8
Slide 14
Addition Method Notice how both equations have a 2y in them one
is positive(top) and one negative(bottom). x + 2y = 8 3x 2y =
8
Slide 15
Addition Method We want to cancel the ys so were left with
nothing but xs so we will add the two equations. x + 2y = 8 3x 2y =
8 ___________ + Add straight down x + 3x + 2y 2y = 8 + 8
Slide 16
Addition Method They cancel and were left with 4x= 16 x + 3x +
2y 2y = 8 + 8
Slide 17
Addition Method Divide each side by four and x = 4 4x = 16 4
4
Slide 18
Addition Method Plug x = 4 back into one of the two starting
equations and you will find the value of y. x + 2y = 8 x = 4 so 4 +
2y = 8 2y = 4 y = 2 Plug in x = 4 Subtract 4 Divide by 2
Slide 19
Addition Method We started off with these two equations and
figured out that x + 2y = 8 3x 2y = 8 x = 4 y = 2
Slide 20
Practice Problem Check Answer Your turn to try one out!!! x +
2y = 3 - x + 3y = 2
Slide 21
Answer If you got this answer advance to next lesson!!! If not,
see worked out solution x = 1 y = 1 Worked Out Solution
Slide 22
Congratulations!!! You have complete the addition method
portion of this unit Great Job! To begin the subtraction method
click on the next button.
Slide 23
Worked Out Solution x + 2y = 3 -x + 3y = 2 _________ 5y = 5 y =
1 x + 2(1) = 3 x = 1 Add the two equations Divide by 5 Plug y = 1
into original equation Subtract 2
Slide 24
Subtraction Method
Slide 25
Practice Problem Try one on your own now 3x 2y = 1 5x 2y =
3
Slide 26
Answer If you got the answer Great Job! If not click on the
worked out solution x = 1 y = 1 Worked Out Solution
Slide 27
Worked Out Solution 3x 2y = 1 5x 2y = 3 _________________ 3x -
5x - 2y + 2y = 1 3 -2x = -2 x = 1 3(1) 2y = 1 -2y = -2 y = 1 -
Subtract bottom equation from top (multiply bottom by (-1) and add)
Simplify Divide by -2 Plug x = 1 into original equation Divide by
-2
Slide 28
Congratulations!!! You have complete the subtraction method
portion of this unit Great Job! To review and begin the quiz Press
the next button.
Slide 29
Summary What have you learned? To add two equations in order to
solve for the two variables in question. To subtract two equations
in order to solve for the two variables. Distinguish between the
two methods. Choose which method to use in different cases and
situations.
Slide 30
Quiz Its Quiz Time Once you begin the quiz you will not be able
to back out so make sure youre ready! Good Luck!
Slide 31
Quiz ? # 1 Which Method would you use to solve this set of
equations? A. Addition Method Addition Method B. Subtraction Method
x + 2y = 3 x 2y = -1
Slide 32
Try Again Oh manUsing the subtraction method wouldnt eliminate
any variables.
Slide 33
Congratulations!!! Exactly Right!!!!! Time for question 2
Slide 34
Quiz ? # 2 Solve these equations: A. x= 1, y = 5 x= 1, y = 5 x
+ 2y = 3 x 2y = -1 B. x= 1, y = 1 D. x= 5, y = 1 C. x= 1, y = 2
Hint
Slide 35
Hint x = 1 Plug back into original equation
Slide 36
Try Again Sorry y does not equal 5 Try Again Hint
Slide 37
Try Again Sorry y does not equal 2 Try Again Hint
Slide 38
Try Again Sorry x does not equal 5 Try Again Hint
Slide 39
Congratulations!!! Exactly Right!!!!! Time for question 3
Slide 40
Quiz ? # 3 Which Method would you use to solve this set of
equations? A. Addition Method Addition Method B. Subtraction Method
3y + 2x = 3 4y + 2x = 4
Slide 41
Try Again Oh man using the addition method wouldnt eliminate
any vairables. Hint
Slide 42
Congratulations!!! Exactly Right!!!!! Time for question 4
Slide 43
Quiz ? # 4 Solve these equations: A. x= 0, y = 1 x= 0, y = 1 3y
+ 2x = 3 4y + 2x = 4 B. x= 1, y = 0 D. x= 1, y = 2 C. x= 3, y = 1/3
Hint
Slide 44
Hint y = 1 Plug back into original equation
Slide 45
Try Again Sorry x does not equal 1 Try Again Hint
Slide 46
Try Again Sorry x does not equal 3 Try Again Hint
Slide 47
Try Again Sorry x does not equal 1 Try Again Hint
Slide 48
Congratulations!!! You Passed the Quiz!!! Youre an All- Star
Mathematician
Slide 49
Back to Home
Slide 50
Works Cited
http://school.discoveryeducation.com/clipart/clip/calcltr.html
http://www.sosmath.com/soe/SE2001/SE2001.html
Slide 51
Home Intro Addition Method Subtraction Method Everything is
complete except the Quiz! Good Luck! CompleteComplete
Slide 52
Home Intro Addition Method Subtraction Method You have finished
the entire lesson! Good Luck in your future mathematical endeavors.
CompleteCompleteComplete Works Cited