ANSWER
The system consists of parallel lines. Both lines have the same slope.
EXPLANATION.
The first equation is
[tex]y = \frac{1}{3} x - 4[/tex]
This equation is in the slope-intercept form.
The second equation is
[tex]3y - x = - 7[/tex]
We write this one too in slope-intercept form so that we can make comparison.
[tex] \implies \: y = \frac{1}{3} x - \frac{7}{3} [/tex]
We can see that both equations have slope
[tex]m = \frac{1}{3} [/tex]
This means the two lines are parallel.
The two lines have different y-intercepts.
Two parallel lines with different y-intercepts will never meet.
The lines will never intersect.
Answer:
The true statements are:
- The system consists of parallel lines
- Both lines have the same slope
Step-by-step explanation:
* Lets talk about the solution of the linear equations
- There are three types of the solutions of the system of linear equations
# If the two lines intersect each other, then there is one solution
- The equations are ax+ by = c , dx + ey = f
# If the two lines parallel to each other, then there is no solution
- The equations are ax+ by = c , ax + by = d in its simplest form ,
 where a is the coefficient of x , b is the coefficient of y and
 c , d are the numerical terms
# If the two lines coincide (over each other), then there are infinite
  solutions
- The equations are ax+ by = c , ax + by = c in its simplest form, where
 a is the coefficient of x , b is the coefficient of y and c is the
 numerical term
* Lets solve the problem
∵ The system of equation is:
  y = 1/3 x - 4 ⇒ (1)
  3y - x = -7 ⇒ (2)
- Lets put equation (1) in the form of equation (2)
∵ y = 1/3 x - 4 ⇒ multiply both sides by 3
∴ 3y = x - 12 ⇒ subtract x from both sides
∴ 3y - x = -12
∴ Equation (1) is 3y - x = -12
∵ Equation (2) is 3y - x = -7
∵ The coefficients of x and y in the two equation are equal
∵ The numerical terms in the two equations are not equal
∴ The equations have no solution because their lines are parallel
∵ The parallel lines have same slope
* The true statements are
- The system consists of parallel lines
- Both lines have the same slope
