Questions: Solve the system of equations by the substitution method. 4x + 2y = 4 -2x = y + 4 Select the correct choice below and, if necessary, fill in the answer box to complete y A. The solution is (Type an ordered pair. Simplify your answer.) B. There are infinitely many solutions. C. There is no solution.

Solve the system of equations by the substitution method. 4x + 2y = 4 -2x = y + 4 Select the correct choice below and, if necessary, fill in the answer box to complete y A. The solution is (Type an ordered pair. Simplify your answer.) B. There are infinitely many solutions. C. There is no solution.
Transcript text: Solve the system of equations by the substitution method. \[ \left\{\begin{array}{l} 4 x+2 y=4 \\ -2 x=y+4 \end{array}\right. \] Select the correct choice below and, if necessary, fill in the answer box to complete y A. The solution is $\square$ (Type an ordered pair. Simplify your answer.) B. There are infinitely many solutions. C. There is no solution.
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Solution

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Solution Steps

Step 1: Solve the second equation for \( y \)

The second equation is: \[ -2x = y + 4 \] Solve for \( y \): \[ y = -2x - 4 \]

Step 2: Substitute \( y \) into the first equation

The first equation is: \[ 4x + 2y = 4 \] Substitute \( y = -2x - 4 \) into the first equation: \[ 4x + 2(-2x - 4) = 4 \]

Step 3: Simplify and solve for \( x \)

Expand and simplify the equation: \[ 4x - 4x - 8 = 4 \] \[ -8 = 4 \] This is a contradiction, which means there is no solution to the system of equations.

Step 4: Determine the correct choice

Since the system has no solution, the correct choice is: \[ \text{C. There is no solution.} \]

Final Answer

C. There is no solution.

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