Question

solve the system of equations graphically. \\(\

$$\begin{cases} y = 3x - 12 \\\\ y = 4x + 3 \\end{cases}$$

\\) graph the equations \\(y = 3x - 12\\) and \\(y = 4x + 3\\) using a graphing utility. choose the correct graph below. \\(\bigcirc\\) a. \\(\bigcirc\\) b. \\(\bigcirc\\) c. \\(\bigcirc\\) d. all graphs are shown in \\(-24, 6\\) by \\(-80, 20\\) viewing windows with \\(\text{xscl} = 2\\) and \\(\text{yscl} = 5\\).

Explanation:

Step1: Find intersection algebraically

Set $3x - 12 = 4x + 3$
$3x - 4x = 3 + 12$
$-x = 15$
$x = -15$
Substitute $x=-15$ into $y=3x-12$:
$y=3(-15)-12=-45-12=-57$
Intersection point: $(-15, -57)$

Step2: Check y-intercepts

For $y=3x-12$, y-intercept is $(0, -12)$
For $y=4x+3$, y-intercept is $(0, 3)$

Step3: Match to graph

The correct graph must show two lines crossing at $(-15, -57)$ (within $[-80,20]$ x-range) with y-intercepts at $(0,-12)$ and $(0,3)$. Option A has two distinct lines with these intercepts and intersecting in the correct region.

Answer:

A. <The graph labeled A with two lines intersecting in the lower left region of the viewing window>