[tex]\bold{\huge{\pink{\underline{ Solution }}}}[/tex]
We have given in the question that,
- The sum of 2 numbers is equal to 11
- The difference between two numbers is 19 .
[tex]\bold{\underline{ To \: Find }}[/tex]
- We have to find the value of x and y.
[tex]\bold{\underline{ Let's \: Begin }}[/tex]
Let the two numbers be x and y
According to the question,
[tex]\sf{ x + y = 11......eq(1) }[/tex]
[tex]\sf{ x - y = 19......eq(2) }[/tex]
Solving eq( 1 ) we get :-
[tex]\sf{ x + y = 11 }[/tex]
[tex]\sf{ x = 11 - y ......eq(3 ) }[/tex]
Subsituting eq(3 ) in eq(2) :-
[tex]\sf{ x - y = 19 }[/tex]
[tex]\sf{ ( 11 - y) - y = 19 }[/tex]
[tex]\sf{ 11 - y - y = 19 }[/tex]
[tex]\sf{ 11 - 2y = 19 }[/tex]
[tex]\sf{ - 2y = 19 - 11 }[/tex]
[tex]\sf{ - 2y = 8}[/tex]
[tex]\sf{ y = 8/(-2) }[/tex]
[tex]\sf{ y = - 4 }[/tex]
[tex]\sf{\red{Thus ,\: the\: value\: of \: y = -4}}[/tex]
Now, Subsitute the value of y in eq( 3 ) :-
[tex]\sf{ x = 11 - y }[/tex]
[tex]\sf{ x = 11 - (-4 ) }[/tex]
[tex]\sf{ x = 11 + 4 }[/tex]
[tex]\sf{ x = 15 }[/tex]
Hence, The value of x and y are 15 and (-4) .
