Question

which statement is true about the system $2x - 4y = -6$ and $y = x + 1$?

• $(5, 4)$ is a solution to one equation but not the other one, so it is not a solution to the system.
• $(5, 4)$ is a solution to both equations, so it is a solution to the system.
• $(5, 4)$ is not a solution to either equation, so it is not a solution to the system.
• $(5, 4)$ is a solution to one equation but not the other one, so it is a solution to the system.

Explanation:

Step1: Check the first equation \(2x - 4y = -6\)

Substitute \(x = 5\) and \(y = 4\) into the equation:
Left - hand side (LHS) \(= 2\times5-4\times4=10 - 16=-6\)
Right - hand side (RHS) \(=-6\)
Since \(LHS = RHS\), \((5,4)\) is a solution to the equation \(2x - 4y=-6\).

Step2: Check the second equation \(y=x + 1\)

Substitute \(x = 5\) and \(y = 4\) into the equation:
Left - hand side (LHS) \(=4\)
Right - hand side (RHS) \(=5 + 1=6\)
Since \(LHS
eq RHS\), \((5,4)\) is not a solution to the equation \(y=x + 1\).

A solution to a system of equations must be a solution to all the equations in the system. Since \((5,4)\) is a solution to one equation (\(2x-4y = - 6\)) but not the other (\(y=x + 1\)), it is not a solution to the system.

Answer:

(5, 4) is a solution to one equation but not the other one, so it is not a solution to the system.