2 Equations with 2 Unknowns

Home

IntroAddition MethodSubtraction MethodYou have finished the entire lesson! Good Luck in your future mathematical endeavors.CompleteCompleteCompleteWorks CitedIntro Video

Try Again

Sorry x does not equal 1 Try Again

HintTry Again

Sorry x does not equal 3 Try Again

HintWelcome

Hey everybody! My name is Cal Culator but all my friends call me Cal. I will be helping you throughout this lesson.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 + 20xAdvance to see the worked out solution.Worked Out SolutionStarting Equation: 5 = 5y + 20x

Subtract 20x from both sides: 5 20x = 5y + 20x 20x

5 20x = 5y

Divide by 5: 1 4x = yLesson PreviewIn this lesson you will learnTo 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.By the end of this lesson you will have...Learned each method and its basics.Practiced each method several time.Taken a final quiz to assess your new knowledge.Lesson PreviewWhy are we learning this?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.It is an essential skill that must be mastered.Real World ApplicationI know some of you are asking When are we ever going to need to do this in real life?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.OverviewThe addition and subtraction methods are part of the elimination method.The whole premise of this elimination method is to A) manipulate both equations to put all the variables on the same side.B) solve for a variable by eliminating the other variable.C) solve for the other variable by plugging back into the original equation.Addition Method

Notice how both equations have a 2y in them one is positive(top) and one negative(bottom). x + 2y = 83x 2y = 8Addition Method

We want to cancel the ys so were left with nothing but xs so we will add the two equations. x + 2y = 83x 2y = 8___________+Add straight downx + 3x + 2y 2y = 8 + 8Addition Method

They cancel and were left with 4x= 16x + 3x + 2y 2y = 8 + 8Addition Method

Divide each side by four andx = 44x = 1644Addition Method

Plug x = 4 back into one of the two starting equations and you will find the value of y.x + 2y = 8x = 4 so4 + 2y = 82y = 4y = 2Plug in x = 4

Subtract 4

Divide by 2Addition Method

We started off with these two equations and figured out that x + 2y = 83x 2y = 8x = 4y = 2Practice ProblemCheck Answer

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

If you got this answer advance to next lesson!!! If not, see worked out solutionx = 1 y = 1Worked Out SolutionPractice Problem

Try one on your own now3x 2y = 15x 2y = 3Answer

If you got the answer Great Job!If not click on the worked out solutionx = 1y = 1Worked Out SolutionSummaryWhat 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 ? # 1Which Method would you use to solve this set of equations? Addition MethodB. Subtraction Methodx + 2y = 3x 2y = -1Back to Home