Answer:
The numbers are
14
and
7
.
Explanation:
Let the numbers be
x
and
y
.
x
+
y
=
21
x
−
y
=
7
y
=
21
−
x
x
−
(
21
−
x
)
=
7
x
−
21
+
x
=
7
2
x
=
28
x
=
14
∴
14
+
y
=
21
y
=
7
Answer: The required numbers are 14 and 7.
Step-by-step explanation: Given that the sum of two numbers is 21 and their difference is 7.
We are to find the numbers.
Let x and y represents the two numbers.
Then, according to the given information, we have
[tex]x+y=21~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x-y=7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Adding equations (i) and (ii), we get
[tex](x+y)+(x-y)=21+7\\\\\Rightarrow 2x=28\\\\\Rightarrow x=\dfrac{28}{2}\\\\\Rightarrow x=14.[/tex]
From equation (i), we get
[tex]x+y=21\\\\\Rightarrow 14+y=21\\\\\Rightarrow y=21-14\\\\\Rightarrow y=7.[/tex]
Thus, the required numbers are 14 and 7.
