Question

Solve the system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, express x and y in terms of the parameter t.) 3x + 6y = 15 −3x − 6y = −15

Answer 1

Answer:

$x=15-2t\,,\,y=t$

Step-by-step explanation:

Matrix is a rectangular array in which elements are arranged in rows and columns.

If number of rows is m and number of columns is n, then order of the matrix is $m\times n$.

Given:

$3x + 6y = 15\\-3x -6y = -15$

Consider $\begin{pmatrix} 3&6&15\\-3&-6&-15\end{pmatrix}$

Apply row operation:$R_2\rightarrow R_2+R_1$

$\begin{pmatrix} 3&6&15\\0&0&0\end{pmatrix}$

Apply row operation:$R_1\rightarrow \frac{R_1}{3}$

$\begin{pmatrix} 1&2&5\\0&0&0\end{pmatrix}$

So, we get $x+2y=15$

Take $y=t\Rightarrow x=15-2y=15-2t$

So, $x=15-2t\,,\,y=t$

Here, for different values of the parameter t, we get different values of x and y.

So, the system of equations has infinite solutions.