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Sagot :
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]
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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