Give x+3y=6 and 3x+5y=7, what is 8x-2y?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

It is given that x+3y=6 and 3x+5y=7 and we have to determine the value of 8x-2y

x + 3y = 6 ...(1)

3x + 5y = 7 ...(2)

Substitute x = 6 - 3y in (2)

=> 3(6 - 3y) + 5y = 7

=> 18 - 9y + 5y = 7

=> 4y = 11

=> y = 11/4

x = 6 - 33/4 = -9/4

8x - 2y = 8*(-9/4) - 2*(11/4)

=> -18 - 22/4

=> -47/2

The value of 8x - 2y = -47/2

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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

It is given that x+3y=6 and 3x+5y=7.

From x + 3y = 6, x = 6 - 3y

Substitute in 3x + 5y = 7

18 - 9y + 5y = 7

-4y = -11

y = 11/4

x = 6 - 33/4 = -9/4

8x - 2y = -72/4 - 22/4

= -94/4

= -47/2

The value of 8x-2y is -47/2

lesanazadi's profile pic

lesanazadi | College Teacher | eNotes Newbie

Posted on

Dear Artucsonia

From x+3y=6 you can find out the value of x to be

x=6-3y

In the second equation replace x by the value you have just found out, i.e. 6-3y. So the scond equation becomes 3(6-3y)+5y=7. Here you have only one variable , i.e. y. Find out the value of y. [ It will be 11/4]. Then put that value in x=6-3y. You get the value of x. [It will be -9/4] You can then put the vaues of x and y that you have found out in 8x-2y and see it will be -47/2. Best of luck.

 

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll have to determine x and y, to find the value of the difference 8x - 2y.

We'll multiply the 1st equation by -3:

-3x - 9y = -18 (3)

We'll add (3) to (2):

-3x - 9y + 3x + 5y = -18 + 7

We'll eliminate like terms:

-4y = -11

y = 11/4

x = 6 - 3y

x = 6 - 33/4

x = (24-33)/4 => x = -9/4

We'll determine the value of the difference:

8x - 2y = 8*(-9/4) - 2*11/4 = -18 - 11/2

8x - 2y = -47/2

The value of the difference is 8x - 2y = -47/2.

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