Problem

Graph the system below and write its solution. \[ \left\{\begin{array}{l} y=-2 x-3 \\ x-3 y=-5 \end{array}\right. \] Note that you can also answer "No solution" or "Infinitely many" solutions. Solution:

Solution

Step 1 :Rewrite the first equation: \(y=-2x-3\) as \(y+2x=-3\)

Step 2 :Write the augmented matrix: \[\left[\begin{array}{ccc|c} 2 & 1 & -3 \\ 1 & -3 & -5 \end{array}\right]\]

Step 3 :Perform row operations (R2 = R2 - R1): \[\left[\begin{array}{ccc|c} 2 & 1 & -3 \\ 0 & -4 & -2 \end{array}\right]\]

Step 4 :Perform row operations (R2 = R2/(-4)): \[\left[\begin{array}{ccc|c} 2 & 1 & -3 \\ 0 & 1 & 1/2 \end{array}\right]\]

Step 5 :Perform row operations (R1 = R1- R2): \[\left[\begin{array}{ccc|c} 2 & 0 & -4 \\ 0 & 1 & 1/2 \end{array}\right]\]

Step 6 :Perform row operations (R1 = R1/2): \[\left[\begin{array}{ccc|c} 1 & 0 & -2 \\ 0 & 1 & 1/2 \end{array}\right]\]

Step 7 :Read the solution from the matrix: \(x = -2\) and \(y = 1/2\)

From Solvely APP
Source: https://solvelyapp.com/problems/8346/

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