Determine the number of solutions of this system of linear equations: −x+y=3 −2x+2y=3 This question requires you to show your work. (1 point) Responses Infinitely Many Solutions Infinitely Many Solutions One Solution One Solution No Solutions

Answer 1

To determine the number of solutions of the system of linear equations, we can rewrite them in a matrix form:

\[
\begin{bmatrix}
-1 & 1 & | & 3 \\
-2 & 2 & | & 3 \\
\end{bmatrix}
\]

By row reducing the augmented matrix, we get:

\[
\begin{bmatrix}
1 & -1 & | & -3 \\
0 & 0 & | & 3 \\
\end{bmatrix}
\]

This system is inconsistent as the second equation becomes 0=3, which is not possible. Therefore, the system has no solutions.

Therefore, the number of solutions of the system of linear equations is: No Solutions.

Answer 2

which side do i divide2 by

Answer 3

To solve the system of linear equations by row reduction, you would divide the entire second row by -2. This will simplify the matrix into a form where you can clearly see the number of solutions. Let me show you step-by-step:

\[
\begin{bmatrix}
-1 & 1 & | & 3 \\
-2 & 2 & | & 3 \\
\end{bmatrix}
\]

Divide row 2 by -2:

\[
\begin{bmatrix}
-1 & 1 & | & 3 \\
1 & -1 & | & -\frac{3}{2} \\
\end{bmatrix}
\]

Now you can continue the row reduction process to determine the number of solutions.

I hope this clarifies your question. Let me know if you need further assistance.