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HELP twice a number plus twice a second number is 310. The difference between the numbers is 55. Find the numbers by writing and solving a system of equations. Explain how you solved the system. PLEASE HELP ME Thank you!   I got numbers are 182.5 and 127.5 but I don't understand how to set up the system equations



Answer :

Twice a number plus twice a second number is 310.
[tex]2x + 2y = 310[/tex]

The difference between the numbers is 55.
[tex]x-y = 55[/tex]

Divide the first equation by 2 to get a 3rd equation:
[tex]x+y=155[/tex]

Add the second and third equations together:
[tex]x-y=55[/tex]
[tex]x+y=155[/tex]
[tex]2x=210[/tex]
[tex]x=105[/tex]

Put x=105 into the second equation to get:
[tex]105-y=55[/tex]
[tex]y=50[/tex]

So you're answers are x=105 and y=50.
abidemiokin

The numbers by writing and solving a system of equations are 50 and 105

System of equations

Let the unknown numbers be x and y

If twice a number plus twice a second number is 310, then;

2x + 2y = 310

x + y = 155

x = 155 - y

Also, If the difference of the numbers is 55, hence;

x - y = 55

155 - y - y = 55

155 - 2y = 55

-2y = 55 - 505

2y = 100

y = 50

Substitute y = 25 into 1 to have:

x = 155 - 50

x = 105

Hence the numbers by writing and solving a system of equations are 50 and 105

Learn more on system of equations here: https://brainly.com/question/847634

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