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What is the solution of  3x + 4y = 8 and x + y = 2.

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lxsptter | Student, Undergraduate | Valedictorian

Posted May 27, 2013 at 5:01 PM via web

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What is the solution of  3x + 4y = 8 and x + y = 2.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 27, 2013 at 5:03 PM (Answer #1)

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The solution of the set of equations 3x + 4y = 8 and x + y = 2 has to be determined.

x + y = 2

=> x = 2 - y

Substitute for x in 3x + 4y = 8

=> 3(2 - y) + 4y = 8

=> 6 - 3y + 4y = 8

=> y = 2

x = 0

The solution of the the given set of equations is x = 0 and y = 2

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jose26425 | High School Teacher | (Level 1) Adjunct Educator

Posted May 30, 2013 at 2:12 AM (Answer #2)

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This is a classic "system of equations" question. A "system" is basically two lines graphed on the same coordinate plane, and your job is to find the "solution," or where they cross. Your answer should be in the form of a coordinate (x,y).

There are three ways to solve a system: elimination, substitution, or graphing. You can use any of the different ways depending on how the equations are written when they are given to you. All 3 ways will give you the same answer. 

Since 3x + 4y = 8 and x + y = 2 are both written in standard form (meaning "y" is not by itself), the easiest way to find the solution to the system is to use "elimination."

The Steps:

1) Set up the equation as if it were a subtraction/addition problem by lining up the x's and y's

3x + 4y = 8

  x +  y = 2

2) Choose either x or y to get rid of. Let's get rid if x.

3) Get the coefficients in front of x the same. Multiply the entire equation by whatever you need. In this case, I multiply everything in x + y = 2 by 3.

3x + 4y = 8

3x + 3y = 6

4) Subtract the 3x in both equations like a subtraction problem. Subtract your y's and the constants the same way. 

    3x + 4y = 8

-   3x + 3y = 6

_______________

            1y = 2     y =2.

5) You've just found half of the solution!

6) Since the solution is always a pont, you need to find the x of the point. You just found the y. So so far, you know the solution is (x, 2).

7) Substitute y=2 into either original equation. x + y = 2 is eaier, so let's use that one. Solve like a one-step equation for x. 

      x + y =2

      x + 2 = 2

         -2     -2

_________________

         x = 0

8) X= 0. You just found your solution! The two lines cross at (0,2).

 

Hope that helps! Good luck!

 

 

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