Question

solve the system by graphing. if the system does not have one unique solution, also state the number of solutions and whether the system is inconsistent or the equations are dependent.
$y = \frac{1}{3}x - 1$
$x = 3y - 15$
part 1 of 2
graph the lines.

Explanation:

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

Starting with $x = 3y-15$, solve for $y$. Add 15 to both sides: $x + 15=3y$. Then divide by 3: $y=\frac{1}{3}x + 5$.

Step2: Analyze the slopes and y - intercepts

The first equation is $y=\frac{1}{3}x-1$, and the second equation (after rewriting) is $y=\frac{1}{3}x + 5$. The slopes of both lines are $m=\frac{1}{3}$. Since the slopes are equal and the y - intercepts ($b_1=-1$ and $b_2 = 5$) are different, the lines are parallel.

Step3: Determine the number of solutions and consistency

Parallel lines never intersect. So, the system of equations has no solution and is inconsistent.

Answer:

The system has no solution and is inconsistent.