Question

solve the system of equations by graphing.
{y = - 3x + 18
3x - 2y = 0

use the graphing tool to graph the system.
click to enlarge graph

Explanation:

Step1: Rewrite the second - equation in slope - intercept form

Starting with $3x - 2y=0$, solve for $y$.
Subtract $3x$ from both sides: $-2y=-3x$.
Divide both sides by $-2$: $y = \frac{3}{2}x$.

Step2: Find the intersection point by setting the two equations equal

Set $-3x + 18=\frac{3}{2}x$.
Add $3x$ to both sides: $18=\frac{3}{2}x+3x$.
Combine like terms: $18=\frac{3x + 6x}{2}=\frac{9x}{2}$.
Multiply both sides by $\frac{2}{9}$: $x = 4$.

Step3: Find the value of $y$

Substitute $x = 4$ into the first equation $y=-3x + 18$.
$y=-3\times4 + 18=-12 + 18 = 6$.

Answer:

The solution of the system is $(4,6)$.