MATH SOLVE

2 months ago

Q:
# 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 β 5x = 156y β 10x = 30Select one:A. Two parallel lines with positive slopeB. Two parallel lines with negative slopeC. A single line with positive slopeD. A single line with negative slope

Accepted Solution

A:

The given system of equations represent a single line with positive slope. Option C is correctSolution:Given, a system of equations which are shown below,3y β 5x = 15 β (1)
6y β 10x = 30 β (2)
When we observe the above equations, when first equation is multiplied with 2, it results in second equationEqn 1 multiplied with "2" , we getβ 6x - 10x = 30 β eqn 3If 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.[tex]\text { slope }=\frac{-x \text { coefficient }}{y \text { coefficient }}=\frac{-3}{-5}=\frac{3}{5}=\text { positive slope }[/tex]So, the line has a positive slope. Β Thus the given system of equations represent a single line with positive slope. So option C is correct.