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Sagot :
To solve the system of equations using substitution, follow these steps:
1. Identify the system of equations:
[tex]\[ \begin{aligned} 5x + y &= 24 \quad \text{(Equation 1)} \\ y &= 3x \quad \text{(Equation 2)} \end{aligned} \][/tex]
2. Substitute Equation 2 into Equation 1:
Since [tex]\( y = 3x \)[/tex], we can replace [tex]\( y \)[/tex] in Equation 1 with [tex]\( 3x \)[/tex]:
[tex]\[ 5x + (3x) = 24 \][/tex]
3. Combine like terms:
[tex]\[ 5x + 3x = 8x \][/tex]
[tex]\[ 8x = 24 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{24}{8} \][/tex]
[tex]\[ x = 3 \][/tex]
5. Substitute [tex]\( x = 3 \)[/tex] back into Equation 2 to find [tex]\( y \)[/tex]:
[tex]\[ y = 3x \][/tex]
[tex]\[ y = 3(3) \][/tex]
[tex]\[ y = 9 \][/tex]
So, the solution to the system of equations is the ordered pair [tex]\((3, 9)\)[/tex].
Therefore, the correct choice is:
A. The solution set is [tex]\(\{ (3, 9) \} \)[/tex].
1. Identify the system of equations:
[tex]\[ \begin{aligned} 5x + y &= 24 \quad \text{(Equation 1)} \\ y &= 3x \quad \text{(Equation 2)} \end{aligned} \][/tex]
2. Substitute Equation 2 into Equation 1:
Since [tex]\( y = 3x \)[/tex], we can replace [tex]\( y \)[/tex] in Equation 1 with [tex]\( 3x \)[/tex]:
[tex]\[ 5x + (3x) = 24 \][/tex]
3. Combine like terms:
[tex]\[ 5x + 3x = 8x \][/tex]
[tex]\[ 8x = 24 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{24}{8} \][/tex]
[tex]\[ x = 3 \][/tex]
5. Substitute [tex]\( x = 3 \)[/tex] back into Equation 2 to find [tex]\( y \)[/tex]:
[tex]\[ y = 3x \][/tex]
[tex]\[ y = 3(3) \][/tex]
[tex]\[ y = 9 \][/tex]
So, the solution to the system of equations is the ordered pair [tex]\((3, 9)\)[/tex].
Therefore, the correct choice is:
A. The solution set is [tex]\(\{ (3, 9) \} \)[/tex].
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