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Solve the system of equations using substitution.
5x+y= 14
y = 2x
amiable mugisha 05/31/24.
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Select the correct choice below and, if necessary, fill in the answer
choice.
A. The solution is
(Type an ordered pair.)
OB. There are infinitely many solutions.
OC. There is no solution.
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Verified Answer :

GinnyAnswer

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

1. Identify the system of equations:
\(\[ \begin{cases} 5x + y = 14 \quad \text{(Equation 1)} \\ y = 2x \quad \text{(Equation 2)} \end{cases} \]\)

2. Substitute \(\( y \)\) from Equation 2 into Equation 1:
Since Equation 2 gives \(\( y \)\) in terms of \(\( x \)\):
\(\[ y = 2x \]\)
Substitute \(\( y = 2x \)\) into Equation 1:
\(\[ 5x + 2x = 14 \]\)

3. Combine like terms and solve for \(\( x \)\):
\(\[ 7x = 14 \]\)
Divide both sides by 7 to isolate \(\( x \)\):
\(\[ x = \frac{14}{7} \]\)
\(\[ x = 2 \]\)

4. Substitute \(\( x = 2 \)\) back into Equation 2 to find \(\( y \)\):
\(\[ y = 2x \]\)
Substitute \(\( x = 2 \)\):
\(\[ y = 2 \cdot 2 \]\)
\(\[ y = 4 \]\)

5. Write the solution as an ordered pair:
The solution to the system of equations is:
\(\[ (x, y) = (2, 4) \]\)

Therefore, the correct choice is:
A. The solution is \(\((2, 4)\)\).

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