Answer:
(-7 , 5)
Explanation:
For elimination method, you are "eliminating" one of the variables. This is achieved by relegating factors or multiples away so that both given expressions share the same term, which can be "eliminated".
In this case, you have the shared term of 7y. Isolate the term. Note the equal sign, what you do to one side, you do to the other.
For the first equation, Subtract 3x from both sides of the equation:
3x + 7y = 14
3x (-3x) + 7y = 14 (-3x)
7y = -3x + 14
For the second equation, subtract 2x from both sides of the equation:
2x + 7y = 21
2x (-2x) + 7y = 21 (-2x)
7y = -2x + 21
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Note that both of them now share the same result, that being 7y. Using the equivalent system of equations (or expressions), you can solve them.
-3x + 14 = 7y
-2x + 21 = 7y
∴ -3x + 14 = -2x + 21
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Add 2x and subtract 14 from both sides of the equation:
-3x (+2x) + 14 (-14) = -2x (+2x) + 21 (-14)
-3x + 2x = 21 - 14
-x = 7
(-x)/-1 = (7)/-1
x = -7
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Next, plug in -7 as x for one of the given equations to solve for y:
2x + 7y = 21
2(-7) + 7y = 21
First, simply by multiplying 2 with -7:
(2 * -7) + 7y = 21
(-14) + 7y = 21
7y - 14 = 21
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 operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
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First, add 14 to both sides of the equation:
7y - 14 (+14) = 21 (+14)
7y = 21 + 14
7y = 35
Next, divide 7 from both sides of the equation:
(7y)/7 = (35)/7
y = 35/7 = 5
y = 5
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Therefore, (-7 , 5) is your answer.
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