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Use the substitution method to solve the system of equations. Select the correct ordered pair.

[tex]\[
\begin{array}{l}
2x + 4y = 14 \\
x = 3
\end{array}
\][/tex]

A. [tex]\((2, 3)\)[/tex]
B. [tex]\((3, 5)\)[/tex]
C. [tex]\((3, 2)\)[/tex]
D. [tex]\((3, 12)\)[/tex]

Sagot :

GinnyAnswer
To solve the system of equations using the substitution method, follow these steps:

1. We are given the system of equations:
[tex]\[ \begin{cases} 2x + 4y = 14 \\ x = 3 \end{cases} \][/tex]

2. Since the second equation already gives us the value of [tex]\( x \)[/tex], we can substitute this value into the first equation.

Substitute [tex]\( x = 3 \)[/tex] into the first equation:
[tex]\[ 2(3) + 4y = 14 \][/tex]

3. Solve for [tex]\( y \)[/tex]:

Simplify the left-hand side:
[tex]\[ 6 + 4y = 14 \][/tex]

4. Isolate [tex]\( y \)[/tex] by subtracting 6 from both sides:
[tex]\[ 4y = 14 - 6 \][/tex]
[tex]\[ 4y = 8 \][/tex]

5. Divide both sides by 4 to solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{8}{4} \][/tex]
[tex]\[ y = 2 \][/tex]

6. Therefore, the solution to the system of equations is [tex]\( x = 3 \)[/tex] and [tex]\( y = 2 \)[/tex]. This corresponds to the ordered pair [tex]\((3, 2)\)[/tex].

So, the correct answer is:

C. [tex]\((3, 2)\)[/tex]
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