Answer:
x = 7 , y = 3 , or 7 free throws, and 3 3-pointers.
Step-by-step explanation:
James scored a total of 16 points during a basketball. Only free throws and 3-point baskets are used. Free throws = 1 point (x), 3-pointers = 3 points (y).
Set the equations:
16 = x + 3y
10 = x + y
First, isolate the variable x in the second equation. Divide y from both sides of the equation:
10 (-y) = x + y (-y)
x = 10 - y
Next, plug in 10 - y for x in the first equation:
16 = x + 3y
16 = (10 - y) + 3y
Simplify. Combine like terms:
16 = 10 - y + 3y
16 = 10 + (-y + 3y)
16 = 10 + 2y
Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operation, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
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First, subtract 10 from both sides of the equation:
16 (-10) = 10 (-10) + 2y
2y = 16 - 10
2y = 6
Next, divide 2 from both sides:
(2y)/2 = (6)/2
y = 6/2 = 3
Plug in 3 for y in one of the equations:
16 = x + 3y
16 = x + 3(3)
16 = x + 9
Isolate the variable, subtract 9 from both sides of the equation:
16 (-9) = x + 9 (-9)
x = 16 - 9
x = 7
x = 7 , y = 3 , or 7 free throws, and 3 3-pointers.
Plug in to check:
16 = x + 3y
10 = x + y
16 = (7) + 3(3)
16 = 7 + 9
16 = 16 (True)
10 = (7) + (3)
10 = 10 (True).
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