Question

what is a system of linear equations? provide an example with your description.
choose the correct answer below.
a. two equations of the form ax + by = c, a and b not both zero, are called a system of linear equati system. an example is shown below.
\

$$\begin{cases} x + y = 7 \\\\ x - y = 1 \\end{cases}$$

b. any two equations are called a system of linear equations or a linear system. an example is shown
\

$$\begin{cases} xy = 7 \\\\ \\dfrac{x}{y} = 1 \\end{cases}$$

Explanation:

A system of linear equations consists of two or more linear equations (in the form \(Ax + By = C\), where \(A\) and \(B\) are not both zero) that share the same variables. Option A correctly defines it (equations in \(Ax + By = C\) form) and provides a valid linear system example (\(

$$\begin{cases}x + y = 7\\x - y = 1\end{cases}$$

\)). Option B’s example includes non - linear equations (\(xy = 7\) is quadratic, \(\frac{x}{y}=1\) is rational), so it’s incorrect.

Answer:

A. Two equations of the form \(Ax + By = C\), \(A\) and \(B\) not both zero, are called a system of linear equations or a linear system. An example is shown below.
\(

$$\begin{cases}x + y = 7\\x - y = 1\end{cases}$$

\)