Asystem 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

The given system of equations represent a single line with positive slope. Option C is correct

Solution:

Given, a system of equations which are shown below,

3y − 5x = 15 ⇒ (1)

6y − 10x = 30 ⇒ (2)

When we observe the above equations, when first equation is multiplied with 2, it results in second equation

Eqn 1 multiplied with "2" , we get

⇒ 6x - 10x = 30 ⇒ eqn 3

If we notice eqn 2 and eqn 3 are same.

Which means the two line equations represents the same line.

Now let us find the slope of line.

So, the line has a positive slope.  Thus the given system of equations represent a single line with positive slope. So option C is correct.

step-by-step explanation:

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