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sum of two numbers is 15, and their difference is 7

by Denise
(New Orleans)











































Linear Equations

The sum of two numbers is 15, and their difference is 7.

Write a system of linear equations and solve the resulting system.

Let x be the larger number and y be the smaller number.

How do you work out this problem?

Comments for sum of two numbers is 15, and their difference is 7

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Jan 12, 2014
answer
by: Anonymous

x + y = 15
- x - y = 7

2y = 8
2y/2 = 8/2
y = 4

x + 4 = 15
x + 4 - 4 = 15 - 4
x = 11

check
11 + 4 = 15
15 = 15

11 - 4 = 7
7 = 7

Feb 14, 2014
ANSWER TO DENISE QUESTION
by: SIBONISO MDLALOSE

2X+Y=15 AND 2X-Y=7.NOW SOLVING FOR X AND Y SIMULTANEOUSLY.LET Y EQAUL TO 15-2X.THEREFORE 2X-Y=7 WE CAN WRITE IT AS 2X-(15-2X)=7;4X=22;X=11/2.AND Y WILL BE EQAUL TO 4.THEREFORE 2(11/2)+4=15 AND 2(11/2)-4=7.THIS SOLUTION PROVES THAT SUM OF 2NUMBERS IS 15,AND THEIR DIFFERENCE IS 7 ONLY IF X IS A LARGER NUMBER AND Y IS A SMALLER NUMBER.

Mar 30, 2014
number word problem
by: Staff


Answer


x = larger number

y = smaller number

x + y = 15

x - y = 7


use the elimination method to eliminate the y variable, and then solve for x

add the two equations

x + y = 15

x - y = 7

------------------

2x + 0 = 22

solve for x by dividing each side of the equation by 2

2x = 22

2x / 2 = 22 / 2

x = 11

substitute 11 for the value of x in the first equation, and then solve for y

x + y = 15

11 + y = 15

subtract 11 from each side of the equation

11 - 11 + y = 15 - 11

0 + y = 4

y = 4

final answer:

x = 11

y = 4






Thanks for writing.

Staff
www.solving-math-problems.com



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Apr 12, 2019
15 and 7}^ 9 NEW
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Nov 12, 2019
Sum and difference NEW
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Sum of 15 and their difference is 3

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Mar 30, 2020
response NEW
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May 12, 2020
explanation without using algebraic equations NEW
by: Anonymous

x + y = 15 tells you that the set of real numbers can range from 15 to 0. We already know 15 and 0 won't work because 15 - 0 = 15 (not 7).

We need to adjust the 15 and 0 so the difference drops by 8 (the difference of 7 is 15-8). Half of that drop: 4 (8/2 =4) tells us how much to subtract from the greatest possible value (15) and add to the smallest greatest value (0) to decrease the difference between the 2 numbers by 8.

Instead of 15 and 0, we now have 11 and 4. It might help to show the difference between 15 and 0, as well as 11 and 4 on a number line to visualize this. Hope that helps.

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