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In Mathematics / High School | 2025-07-08

Which of these shows the result of using the first equation to substitute for $y$ in the second equation, then combining like terms?

[tex]
\begin{array}{l}
y=3 x \\
3 x+2 y=18
\end{array}
[/tex]

A. [tex]$3 x=18$[/tex]
B. [tex]$3 y=18$[/tex]
C. [tex]$9 x=18$[/tex]
D. [tex]$6 x=18$[/tex]

Asked by carsonbogg

Answer (2)

Substitute y = 3 x into the equation 3 x + 2 y = 18 .
Simplify the equation: 3 x + 2 ( 3 x ) = 18 A rr 3 x + 6 x = 18 .
Combine like terms: 9 x = 18 .
The result of the substitution and simplification is 9 x = 18 ​ .

Explanation

Problem Analysis We are given the system of equations:

y = 3 x 3 x + 2 y = 18
Our goal is to substitute the first equation into the second equation and simplify the result by combining like terms.

Substitution Substitute y = 3 x into the second equation:

3 x + 2 ( 3 x ) = 18
This replaces y in the second equation with its equivalent expression in terms of x .

Simplification Now, simplify the equation by performing the multiplication:

3 x + 6 x = 18
This step expands the equation after the substitution.

Combining Like Terms Combine the like terms on the left side of the equation:

9 x = 18
This combines the x terms to simplify the equation further.

Final Answer The resulting equation after substitution and combining like terms is 9 x = 18 . Comparing this with the given options, we see that it matches option C.

Therefore, the correct answer is C.
Examples
Substitution is a fundamental technique in algebra, and it's used extensively in real-world applications. For instance, consider a scenario where you're trying to optimize a budget. Suppose you know that the cost of materials ( y ) is three times the cost of labor ( x ), expressed as y = 3 x . If your total budget for a project is 3 x + 2 y = 18 (where 3 x represents labor costs and 2 y represents material costs), you can use substitution to determine the optimal allocation between labor and materials. By substituting y = 3 x into the budget equation, you can find the value of x and subsequently determine the value of y , allowing you to make informed decisions about resource allocation.

Answered by GinnyAnswer | 2025-07-08

After substituting y = 3 x into the equation 3 x + 2 y = 18 and simplifying, we get 9 x = 18 . Thus, the correct answer is option C: 9 x = 18 .
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Answered by Anonymous | 2025-07-15

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