Question

A system of equations is shown below. Which of the following statements describes the graph of this system of equations in the (x, y) coordinate plane?
3y − 5x = 15
6y − 10x = 30

Select one:
A. Two parallel lines with positive slope
B. Two parallel lines with negative slope
C. A single line with positive slope
D. A single line with negative slope

Answer 1

Answer:

Option C. will be correct.

Step-by-step explanation:

The equations of straight lines are given as  

3y - 5x = 15 ........... (1)

And, 6y - 10x = 30 ......... (2)

If we divide the equation (2), by 2 then we will get 3y - 5x = 15 which is nothing but the equation (1).

Therefore, those two equations (1) and (2) represents the same straight line.

Now, from equation (1), we can write  $y = \frac{5}{3} x+ 5$.

This is an equation of a straight line in slope-intercept form and here slope is positive.

Therefore, Option C. will be correct. (Answer)