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. So option C is correct.

SOLUTION:

Given system of equations are

`\begin{array}{l}{3 y-5 x=15 \rightarrow(1)} \\\\ {6 y-10 x=30 \rightarrow(2)}\end{array}`

Now, if we observe,
`(1) * 2 \rightarrow(2)` multiplying the
`1^(st)` equation with 2 results in
`2^(nd)` equation.

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.