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

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.

`\text { slope }=\frac{-x \text { coefficient }}{y \text { coefficient }}=(-3)/(-5)=(3)/(5)=\text { positive slope }`

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.