Questions: y=-1/2 x+5 -8 x-4 y=-24 Is (2,4) a solution to the system above? True False

Solution Steps

To determine if \((2, 4)\) is a solution to the given system of equations, we need to substitute \(x = 2\) and \(y = 4\) into both equations and check if both equations hold true.

We start by substituting \(x = 2\) and \(y = 4\) into the first equation:

\[ y = -\frac{1}{2} x + 5 \]

Substituting the values:

\[ 4 = -\frac{1}{2} \cdot 2 + 5 \]

Calculating the right side:

\[ 4 = -1 + 5 \]

This simplifies to:

\[ 4 = 4 \]

Thus, the first equation is satisfied.

Next, we substitute \(x = 2\) and \(y = 4\) into the second equation:

\[ -8x - 4y = -24 \]

Substituting the values:

\[ -8 \cdot 2 - 4 \cdot 4 = -24 \]

Calculating the left side:

\[ -16 - 16 = -32 \]

This simplifies to:

\[ -32 \neq -24 \]

Thus, the second equation is not satisfied.

Since the point \((2, 4)\) satisfies the first equation but does not satisfy the second equation, it is not a solution to the system of equations.

Final Answer