Answer:
The numbers are
5
and
8
Step-by-step explanation:
We know:
m
−
n
=
3
And we know:
m
+
n
=
13
Next, solve the first equation for
m
:
m
−
n
+
n
=
3
+
n
m
−
0
=
3
+
n
m
=
3
+
n
Then, substitute
3
+
n
for
m
in the second equation and solve for
n
:
m
+
n
=
13
becomes:
(
3
+
n
)
+
n
=
13
3
+
2
n
=
13
−
3
+
3
+
2
n
=
−
3
+
13
0
+
2
n
=
10
2
n
=
10
2
n
2
=
10
2
2
n
2
=
5
n
=
5
Now, substitute
5
for
n
in the solution to the first equation and calculate
m
:
m
=
3
+
n
becomes:
m
=
3
+
5
m
=
8
The solution is:
n
=
5
and
m
=
8
[tex]\text{Let the two numbers be x and y}\\\\x+y=3~~~.....(i)\\\\x-y=13~~~.....(ii)\\\\\text{(i)+(ii):}\\\\x+y+x-y = 3+13\\\\\implies 2x = 16 \\\\\implies x = \dfrac{16}2 = 8\\\\\text{(ii)-(i):}\\\\x-y-x-y=13-3\\\\\implies -2y=10\\\\\implies y= -5\\\\\text{Hence the numbers are }~8~\text{and}~ -5[/tex]
