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Lemur [1.5K]
3 years ago
9

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
Mathematics
1 answer:
ollegr [7]3 years ago
5 0

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

<u>SOLUTION: </u>

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) \times 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 }}=\frac{-3}{-5}=\frac{3}{5}=\text { positive slope }

So, the line has a positive slope.

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