Question

solve the system of equations by the substitution method.
\

$$\begin{cases} y = 2x + 1 \\\\ 4y - 6x = 10 \\end{cases}$$

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution is \boxed{}. (simplify your answer. type an ordered pair.)
b. there are infinitely many solutions.
c. there is no solution.

Explanation:

Step1: Substitute \( y = 2x + 1 \) into \( 4y - 6x = 10 \)

Substitute \( y \) in the second equation: \( 4(2x + 1) - 6x = 10 \)

Step2: Simplify the equation

Expand and simplify: \( 8x + 4 - 6x = 10 \)
Combine like terms: \( 2x + 4 = 10 \)
Subtract 4 from both sides: \( 2x = 10 - 4 = 6 \)
Divide by 2: \( x = \frac{6}{2} = 3 \)

Step3: Find \( y \) using \( y = 2x + 1 \)

Substitute \( x = 3 \) into \( y = 2x + 1 \): \( y = 2(3) + 1 = 6 + 1 = 7 \)

Answer:

A. The solution is \( (3, 7) \)