Answer:
x = 53, y = 33
Step-by-step explanation:
Let one of the numbers = x, & the other = y. Set the equations:
x + y = 86
x - y = 20
This is a system of equation, in which the variables must be true for both of them.
First, choose a equation to use. In this case, I will choose x + y = 86. Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract y from both sides.
x + y = 86
x + y (-y) = 86 (-y)
x = 86 - y
Now, note the other equation: x - y = 20. You now know that x = 86 - y. Plug in 86 - y for x in the "other" equation:
x - y = 20
(86 - y) - y = 20
Simplify. Combine like terms:
86 - y - y = 20
86 - 2y = 20
Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS (Parenthesis, Exponents (& Roots), Multiplication, Division, Addition, Subtraction):
First, subtract 86 from both sides:
86 (-86) - 2y = 20 (-86)
-2y = 20 - 86
-2y = -66
Isolate the variable, y. Divide -2 from both sides:
(-2y)/-2 = (-66)/-2
<em>Note: Before we go any further, I want to remind you of division & multiplication rules. There are 3 kinds, when you are multiplying two positive numbers (+/+), when you are multiplying a positive number with a negative number (+/-), and when you are multiplying a two negative numbers (-/-)</em>. <em>Note the "table" in the bottom</em>:
________________________________________________________
(+/+) : Two positive numbers multiplied/divided with each other will always result in a positive answer:
Examples:
10/5 = 2
20/10 = 2
(+/-) : One positive number and one negative number multiplied/divided with each other will always result in a negative answer:
Examples:
20 x -5 = -100
50 x -3 = -150
(-/-) : Two negative numbers multiplied/divided with each other will always result in a positive answer:
Examples:
-30 x -5 = 150
-200/-10 = 20
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Now, solve the equation:
(-2y)/-2 = (-66)/-2
y = -66/-2
Divide.
y = 33
One of your numbers (y) is 33. Plug in 33 for y in one of the equations:
x + y = 86
x + (33) = 86
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract 33 from both sides.
x + 33 (-33) = 86 (-33)
x = 86 - 33
x = 53
Your answers: x = 53, y = 33.
Check: Plug in 53 for x, 33 for y in the equations:
<u>x + y = 86:</u>
(53) + (33) = 86
86 = 86 (True)
<u>x - y = 20</u>:
(53) - (33) = 20
20 = 20 (True)
Your answers: x = 53, y = 33
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