Question

1. graph the system of equations and determine the solution.

$y = -3x - 5$
$x - y = -3$
$\bigcirc$ $(-2,1)$
$\bigcirc$ $(2, -1)$
$\bigcirc$ $(1, -2)$
$\bigcirc$ $(-1, 2)$
clear all

Explanation:

Step1: Rewrite the second equation

We have the second equation \(x - y=-3\), we can rewrite it in slope - intercept form (\(y = mx + b\)) by solving for \(y\).
\(x - y=-3\) can be transformed to \(y=x + 3\) by adding \(y\) to both sides and then adding 3 to both sides.

Step2: Substitute \(y=-3x - 5\) into \(y=x + 3\)

Since we have two equations: \(y=-3x - 5\) and \(y=x + 3\), we can set them equal to each other because they both equal \(y\).
\(-3x-5=x + 3\)

Step3: Solve for \(x\)

Add \(3x\) to both sides of the equation \(-3x-5=x + 3\):
\(-5 = 4x+3\)
Subtract 3 from both sides:
\(-5-3=4x\)
\(-8 = 4x\)
Divide both sides by 4:
\(x=-2\)

Step4: Solve for \(y\)

Substitute \(x = - 2\) into the equation \(y=-3x - 5\) (we could also use \(y=x + 3\)):
\(y=-3\times(-2)-5\)
\(y = 6-5=1\)

Answer:

\((-2,1)\)