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How do you solve for y in \[3x + 2y = 24\] if $x = 5$ ?

seo-qna
Last updated date: 23rd Jul 2024
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Views today: 11.83k
Answer
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Hint: In this question, we are given an algebraic expression containing two unknown variable quantities. We know that to find the value of “n” unknown variables, we need “n” number of equations. In the given algebraic expression, we have 2 unknown quantities but only one equation. As the unknown quantities are variable, we can get different values of one variable on putting different values of the other variable, that is, we can express one variable in terms of the other variable. As we are given the value of x, so we can find the value of y easily by putting the given value in the given expression.

Complete step-by-step solution:
We are given that \[3x + 2y = 24\]
And we are also given that $x = 5$
So, on putting this value of x in the above equation, we get –
$
  3(5) + 2y = 24 \\
   \Rightarrow 15 + 2y = 24 \\
 $
To find the value of y, we will take 15 and 2 to the right-hand side and then apply the arithmetic operations.
$
   \Rightarrow y = \dfrac{{24 - 15}}{2} \\
   \Rightarrow y = \dfrac{9}{2} \\
 $
Hence, when \[3x + 2y = 24\] and $x = 5$ , $y = \dfrac{9}{2}$ .

Note: The mathematical equations that are a combination of numerical values and alphabets are known as algebraic expressions. The alphabets represent some unknown quantities, the alphabets and numerical values are linked via arithmetic operations like addition, subtraction, multiplication and division. The answer obtained is a fraction that is already in simplified form. If the fraction obtained is not in simplified form, then we would cancel out the common factors present in the numerator and the denominator.