Answer :
To solve the system of equations using substitution, follow these steps:
1. Identify the system of equations:
[tex]\[ \begin{cases} 5x + y = 14 \quad \text{(Equation 1)} \\ y = 2x \quad \text{(Equation 2)} \end{cases} \][/tex]
2. Substitute [tex]\( y \)[/tex] from Equation 2 into Equation 1:
Since Equation 2 gives [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
[tex]\[ y = 2x \][/tex]
Substitute [tex]\( y = 2x \)[/tex] into Equation 1:
[tex]\[ 5x + 2x = 14 \][/tex]
3. Combine like terms and solve for [tex]\( x \)[/tex]:
[tex]\[ 7x = 14 \][/tex]
Divide both sides by 7 to isolate [tex]\( x \)[/tex]:
[tex]\[ x = \frac{14}{7} \][/tex]
[tex]\[ x = 2 \][/tex]
4. Substitute [tex]\( x = 2 \)[/tex] back into Equation 2 to find [tex]\( y \)[/tex]:
[tex]\[ y = 2x \][/tex]
Substitute [tex]\( x = 2 \)[/tex]:
[tex]\[ y = 2 \cdot 2 \][/tex]
[tex]\[ y = 4 \][/tex]
5. Write the solution as an ordered pair:
The solution to the system of equations is:
[tex]\[ (x, y) = (2, 4) \][/tex]
Therefore, the correct choice is:
A. The solution is [tex]\((2, 4)\)[/tex].
1. Identify the system of equations:
[tex]\[ \begin{cases} 5x + y = 14 \quad \text{(Equation 1)} \\ y = 2x \quad \text{(Equation 2)} \end{cases} \][/tex]
2. Substitute [tex]\( y \)[/tex] from Equation 2 into Equation 1:
Since Equation 2 gives [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
[tex]\[ y = 2x \][/tex]
Substitute [tex]\( y = 2x \)[/tex] into Equation 1:
[tex]\[ 5x + 2x = 14 \][/tex]
3. Combine like terms and solve for [tex]\( x \)[/tex]:
[tex]\[ 7x = 14 \][/tex]
Divide both sides by 7 to isolate [tex]\( x \)[/tex]:
[tex]\[ x = \frac{14}{7} \][/tex]
[tex]\[ x = 2 \][/tex]
4. Substitute [tex]\( x = 2 \)[/tex] back into Equation 2 to find [tex]\( y \)[/tex]:
[tex]\[ y = 2x \][/tex]
Substitute [tex]\( x = 2 \)[/tex]:
[tex]\[ y = 2 \cdot 2 \][/tex]
[tex]\[ y = 4 \][/tex]
5. Write the solution as an ordered pair:
The solution to the system of equations is:
[tex]\[ (x, y) = (2, 4) \][/tex]
Therefore, the correct choice is:
A. The solution is [tex]\((2, 4)\)[/tex].