2 Equations with 2 Unknowns Created by Daniel Seiltz Click Me to Begin!

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!

Welcome Hey everybody! My name is Cal Culator but all my friends call me Cal. I will be helping you throughout this lesson.

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

Intro Video

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.

Review Problem Solve the equation for y. 5 = 5y + 20x Advance to see the worked out solution.

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

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.

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.

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.

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.

Addition Method Start with two equations with two variables like these. x + 2y = 8 3x – 2y = 8

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

Addition Method We want to cancel the y’s so were left with nothing but x’s so we will add the two equations. x + 2y = 8 3x – 2y = 8 ___________ + Add straight down… x + 3x + 2y – 2y = 8 + 8

Addition Method They cancel and we’re left with … 4x= 16 x + 3x + 2y – 2y = 8 + 8

Addition Method Divide each side by four and… x = 4 4x =

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…

Addition Method We started off with these two equations and figured out that… x + 2y = 8 3x – 2y = 8 x = 4 y = 2

Practice Problem Check Answer Your turn to try one out!!! x + 2y = 3 - x + 3y = 2

Answer If you got this answer advance to next lesson!!! If not, see worked out solution x = 1 y = 1 Worked Out Solution

Congratulations!!! You have complete the addition method portion of this unit… Great Job! To begin the subtraction method click on the next button.

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…

Subtraction Method

Practice Problem Try one on your own now… 3x – 2y = 1 5x – 2y = 3

Answer If you got the answer… Great Job! If not click on the worked out solution x = 1 y = 1 Worked Out Solution

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

Congratulations!!! You have complete the subtraction method portion of this unit… Great Job! To review and begin the quiz… Press the next button.

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.

Quiz Its Quiz Time… Once you begin the quiz you will not be able to back out so make sure you’re ready! Good Luck!

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

Try Again Oh man…Using the subtraction method wouldn’t eliminate any variables.

Congratulations!!! Exactly Right!!!!! Time for question 2…

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

Hint x = 1 Plug back into original equation

Try Again Sorry… y does not equal 5… Try Again Hint

Try Again Sorry… y does not equal 2… Try Again Hint

Try Again Sorry… x does not equal 5… Try Again Hint

Congratulations!!! Exactly Right!!!!! Time for question 3…

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

Try Again Oh man… using the addition method wouldn’t eliminate any vairables. Hint

Congratulations!!! Exactly Right!!!!! Time for question 4…

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

Hint y = 1 Plug back into original equation

Try Again Sorry… x does not equal 1… Try Again Hint

Try Again Sorry… x does not equal 3… Try Again Hint

Try Again Sorry… x does not equal 1… Try Again Hint

Congratulations!!! You Passed the Quiz!!! You’re an All- Star Mathematician

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Works Cited

Home Intro Addition Method Subtraction Method Everything is complete except the Quiz! Good Luck! CompleteComplete

Home Intro Addition Method Subtraction Method You have finished the entire lesson! Good Luck in your future mathematical endeavors. CompleteCompleteComplete Works Cited