Larger number:
smaller number:

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

Larger number: 35

Smaller number: 14

hope this helps

step-by-step explanation:

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step-by-step explanation: