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

Answer

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Answer

Read the solution from the matrix: $x = - 2$ and $y = 1 / 2$

Steps

Step 1 ：Rewrite the first equation: $y = - 2 x - 3$ as $y + 2 x = - 3$

Step 2 ：Write the augmented matrix: $[\begin{array}{cccc} 2 & 1 & - 3 \\ 1 & - 3 & - 5 \end{array}]$

Step 3 ：Perform row operations (R2 = R2 - R1): $[\begin{array}{cccc} 2 & 1 & - 3 \\ 0 & - 4 & - 2 \end{array}]$

Step 4 ：Perform row operations (R2 = R2/(-4)): $[\begin{array}{cccc} 2 & 1 & - 3 \\ 0 & 1 & 1 / 2 \end{array}]$

Step 5 ：Perform row operations (R1 = R1- R2): $[\begin{array}{cccc} 2 & 0 & - 4 \\ 0 & 1 & 1 / 2 \end{array}]$

Step 6 ：Perform row operations (R1 = R1/2): $[\begin{array}{cccc} 1 & 0 & - 2 \\ 0 & 1 & 1 / 2 \end{array}]$

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