Question

A. 5x+y=-310x +2y=-6QUESTIONS•M=SLOPE YINT•NUMBER OF SOLUTIONS

Answer 1

ANSWERS

• m =, -5

,

• y-intercept = ,-3

,

• Number of solutions: ,infinite solutions ,(many solutions)

Step-by-step explanation

Note that the second equation of this system is the first equation multiplied by 2:

`\begin{gathered} 2\cdot(5x+y=-3) \\ 2\cdot5x+2y=-2\cdot3 \\ 10x+2y=-6 \end{gathered}`

This means that these two equations represent the same line. If they are both the same line, then they intersect in infinite points, so the system has infinite solutions.

On the other hand, both equations have the same slope and y-intercept. If we rewrite the first equation in slope-intercept form, by clearing y, we can see them more easily:

`\begin{gathered} 5x+y=-3 \\ y=-5x-3 \end{gathered}`

The slope is -5 and the y-intercept is -3