Questions: Solve the system by the substitution method. x-2 y =-3 y =-4 x+24 Select the correct choice below and fill in any answer boxes present in your choice. A. The solution is (Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.

Solution Steps

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

1. Substitute the expression for \( y \) from the second equation into the first equation.
2. Solve the resulting equation for \( x \).
3. Substitute the value of \( x \) back into the second equation to find the value of \( y \).
4. Verify the solution by plugging the values of \( x \) and \( y \) into both original equations.

We start with the following system of equations: \[ \begin{aligned}

1. & \quad x - 2y = -3 \\
2. & \quad y = -4x + 24 \end{aligned} \]

We substitute the expression for \( y \) from the second equation into the first equation: \[ x - 2(-4x + 24) = -3 \] This simplifies to: \[ x + 8x - 48 = -3 \] or \[ 9x - 48 = -3 \]

Next, we solve for \( x \): \[ 9x = 45 \quad \Rightarrow \quad x = 5 \]

Now, we substitute \( x = 5 \) back into the second equation to find \( y \): \[ y = -4(5) + 24 = -20 + 24 = 4 \]

Final Answer