SOLUTION: Solving Systems Using Elimination. Your math test has 38 questions and is worth 200 points. The test consist of multiple choice questions worth 4 points each and open ended questio

Question 1149916: Solving Systems Using Elimination. Your math test has 38 questions and is worth 200 points. The test consist of multiple choice questions worth 4 points each and open ended questions worth 20 points each. How many of each type of question are there?
So far I have
x + y = 38
4x +20y = 200

Answer by ikleyn(52794) (Show Source): You can put this solution on YOUR website!
.


Your start is fine.


The next steps are

     x +  y =   38    (1)
    4x + 20y = 200    (2)


To solve by Elimination, multiply equation (1) by 4 (both sides). Keep equation (2) as is.


    4x + 4y =  4*38   (1')
    4x + 20y = 200    (2')


Now subtract equation (1') from equation (2').  The terms " 4x " will kill each other, and you will get single equation 
for variable "y" only (!)


         20y - 4y = 200 - 4*38 

         16y      = 48

           y      = 48/16 = 3.


It how the Elimination method works.


Finally, substitute the value y= 3 into equation (1) to get "x".


          x + 3 = 38

          x     = 38-3 = 35.


ANSWER.  x= 35;  y= 3.

Solved.

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In this site, there is a large group of lessons on solving 2x2-system of linear equations
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    - Solution of the linear system of two equations in two unknowns by the Elimination method
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    - Geometric interpretation of the linear system of two equations in two unknowns
    - Useful tricks when solving systems of 2 equations in 2 unknowns by the Substitution method
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    - OVERVIEW of lessons on solving systems of two linear equations in two unknowns

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Systems of two linear equations in two unknowns".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

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