If the sum of two integers is 10 and their difference is 4, the integers are 7 and 3
Let the two integers be x and y
If the sum of the integers is 10, hence:
[tex]x+y=10 ........................... 1[/tex]
If the difference of the integers is 4, then:
[tex]x - y = 4 ................... 2[/tex]
Solve both equations simultaneously:
Add equations 1 and 2:
[tex]x+x = 10+4\\2x = 14\\x = 14/2\\x = 7[/tex]
Substitute x = 7 into equation 1:
From 1:
[tex]x +y=10\\7+y=10\\y=10-7\\y=3[/tex]
This shows that the two integers are 7 and 3
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