Question

valerie had the following system of equations in her math homework. equation 1: $y = 2.5x + 4.5$ equation 2: $y = 5x + 7$ valerie claims $(-1,2)$ is a solution to the system of equations. is valerie correct? $\bigcirc$ yes. $(-1,2)$ is a solution to the second equation, so it is a solution to the system of equations. $\bigcirc$ no. $(-1,2)$ is not a solution to the first equation, so it is not a solution to the system of equations. $\bigcirc$ yes. $(-1,2)$ is a solution to both equations, so it is a solution to the system of equations. $\bigcirc$ no. $(-1,2)$ is not a solution to the second equation, so it is not a solution to the system of equations.

Explanation:

Step1: Check Equation 1

Substitute \( x = -1 \), \( y = 2 \) into \( y = 2.5x + 4.5 \).
Right - hand side: \( 2.5\times(-1)+4.5=-2.5 + 4.5 = 2 \), which equals the left - hand side \( y = 2 \). So \((-1,2)\) is a solution to Equation 1.

Step2: Check Equation 2

Substitute \( x=-1\), \( y = 2 \) into \( y=5x + 7 \).
Right - hand side: \( 5\times(-1)+7=-5 + 7=2 \), which equals the left - hand side \( y = 2 \). So \((-1,2)\) is a solution to Equation 2.
Since \((-1,2)\) is a solution to both equations, it is a solution to the system of equations.

Answer:

Yes. \((-1,2)\) is a solution to both equations, so it is a solution to the system of equations.