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
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.
which side do i divide2 by
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.