Question

solve the system of equations by graphing.
$\begin{cases}y = 3x - 18\\-3x - 2y = 0end{cases}$
use the graphing tool to graph the system.

Explanation:

Step1: Rewrite the second - equation

Rewrite $-3x - 2y=0$ in slope - intercept form $y=mx + b$. First, solve for $y$:
$-2y=3x$, so $y =-\frac{3}{2}x$.

Step2: Identify key points for the first equation

For $y = 3x-18$, when $x = 0$, $y=-18$; when $y = 0$, $3x-18=0$, then $3x=18$ and $x = 6$. So two points on the line $y = 3x-18$ are $(0,-18)$ and $(6,0)$.

Step3: Identify key points for the second equation

For $y=-\frac{3}{2}x$, when $x = 0$, $y = 0$; when $x = 2$, $y=-3$. So two points on the line $y=-\frac{3}{2}x$ are $(0,0)$ and $(2,-3)$.

Step4: Graph and find the intersection

Graph the two lines $y = 3x-18$ and $y=-\frac{3}{2}x$. The intersection point of the two lines is the solution of the system of equations.
We can also solve the system algebraically. Substitute $y = 3x-18$ into $-3x - 2y=0$:
$-3x-2(3x - 18)=0$.
Expand: $-3x-6x + 36=0$.
Combine like - terms: $-9x=-36$.
Solve for $x$: $x = 4$.
Substitute $x = 4$ into $y = 3x-18$, then $y=3\times4-18=12 - 18=-6$.

Answer:

$(4,-6)$