Question

a system of equations is shown.
$y = 3x - 5$
$y = \frac{1}{2}x$
which statement is true about the ordered pair $(1,2)$?
\bigcirc $(1,2)$ is a solution to the system of equations because it is a solution to the second equation.
\bigcirc $(1,2)$ is a solution to the system of equations because it is a solution to both equations.
\bigcirc $(1,2)$ is not a solution to the system of equations because it is not a solution to either equation.
\bigcirc $(1,2)$ is a solution to the system of equations because it is a solution to the first equation.

Explanation:

Step1: Check first equation

Substitute \(x = 1\), \(y = 2\) into \(y = 3x - 5\).
Left side: \(y = 2\).
Right side: \(3(1)-5 = 3 - 5 = -2\).
Since \(2
eq -2\), \((1,2)\) is not a solution to the first equation.

Step2: Check second equation

Substitute \(x = 1\), \(y = 2\) into \(y=\frac{1}{2}x\).
Left side: \(y = 2\).
Right side: \(\frac{1}{2}(1)=\frac{1}{2}\).
Since \(2
eq\frac{1}{2}\), \((1,2)\) is not a solution to the second equation.

Wait, there's a mistake above. Wait, let's re - check:

Wait, for the first equation \(y = 3x-5\), when \(x = 1\), \(y=3\times1 - 5=-2
eq2\).

For the second equation \(y=\frac{1}{2}x\), when \(x = 1\), \(y=\frac{1}{2}\times1 = 0.5
eq2\).

So \((1,2)\) is not a solution to either equation. So the correct option is " \((1,2)\) is not a solution to the system of equations because it is not a solution to either equation."

Answer:

\((1,2)\) is not a solution to the system of equations because it is not a solution to either equation.