Question

makai had the following system of equations in his math homework: equation 1: $y = 2x - 10$ equation 2: $y = \frac{1}{2}x - 5$ makai claims $(0, -5)$ is a solution to the system of equations. is makai correct? \bigcirc no: $(0, -5)$ is not a solution to the second equation, so it is not a solution to the system of equations. \bigcirc no: $(0, -5)$ is not a solution to the first equation, so it is not a solution to the system of equations. \bigcirc yes: $(0, -5)$ is a solution to the second equation, so it is a solution to the system of equations. \bigcirc yes: $(0, -5)$ is a solution to both equations, so it is a solution to the system of equations.

Explanation:

Step1: Check Equation 1

Substitute \( x = 0 \), \( y = -5 \) into \( y = 2x - 10 \).
Left side: \( y = -5 \), Right side: \( 2(0) - 10 = -10 \).
Since \( -5
eq -10 \), \( (0, -5) \) is not a solution to Equation 1.

Step2: Check Equation 2 (optional, but for system)

A solution to a system must satisfy all equations. Since it fails Equation 1, we can conclude.

Answer:

No, (0, -5) is not a solution to the first equation, so it is not a solution to the system of equations. (The option with this description)