Answer :

The answers are 347 and 865. To solve this problem you set up two equations,
x+y=1212 and x-y=518. You then get the second x by itself by adding y to both sides. You then have x+y=1212 and x=y+518. After this you substitute the x into the first equation and have y+518+y=1212. Then simplify to 2y=694 and y=347
Now that y=347 you put it in the original equation. Solve and get that x=865

The required two numbers are 865 and 347.

What is sum?

"It is the result of adding two or more mathematical expressions / numbers together."

What is difference?

"It is the result of subtracting one mathematical expression / number from another."

What is system of equations?

"A system of equations is a finite set of equations for which we find the common solution."

For given example,

Let, x, y be two numbers.

Two numbers have the sum of 1212

⇒ x + y =1212                           .....................(1)

Two numbers have the difference of 518

⇒ x - y = 518                             .....................(2)

So, we have the system of equations as

x + y = 1212

x - y = 518

From equation (2) we get,

x = 518 + y                             ............................(3)

Substitute this value in equation (1),

⇒ (518 + y) + y = 1212

⇒ 518 + 2y = 1212

⇒ 2y = 1212 - 518

⇒ 2y = 694

⇒ y = 694/2

⇒ y = 347

Substitute this value of 'y' in equation (3),

⇒ x = 518 + 347

⇒ x = 865

Therefore, the required two numbers are 865 and 347.

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