Let:
Larger number = x
Smaller number = y
-------------------------------------------------------------------------------------------------------------------
x + y = 49
x - y = 21
-------------------------------------------------------------------------------------------------------------------
Isolate the x in the first equation. Subtract y from both sides
x + y (-y) = 49 (-y)
x = 49 - y
-------------------------------------------------------------------------------------------------------------------
Now that we know what x is, plug in 49 - y (which = x) into x in the other equation.
x - y = 21
(49 - y) -y = 21
Simplify.
49 -2y = 21
Note the equal sign. What you do to one side, you do to the other. Do the opposite of PEMDAS. First subtract 49 from both sides
-2y +49 (-49) = 21 (-49)
-2y = 21 - 49
-2y = -28
Next, divide -2 from both sides to isolate the y
-2y/-2 = -28/-2
y = -28/-2
y = 14
-------------------------------------------------------------------------------------------------------------------
Now that we know what y is, plug into one of the equations.
x + y = 49
x + (14) = 49
Isolate the x. Subtract 14 from both sides
x + 14 (-14) = 49 (-14)
x = 49 (-14)
Simplify
x = 35
-------------------------------------------------------------------------------------------------------------------
Answer:
Larger number: 35
Smaller number: 14
-------------------------------------------------------------------------------------------------------------------
hope this helps
