Question

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.

y=-5x+1
y=-2x-2

Answer 1

Second option: One solution. Independent.

Explanation:

The equation of the line in Slope-Intercept form is:

`y=mx+b`

Where "m" is the slope and "b" is the y-intercept.

Since the equations of the system have this form, we know that they are lines.

We can identify that the y-intercept of the first equation
`y=-5x+1` is:

`b=1`

Now we need to find the x-intercept. Substitute
`y=0` and solve for "x":

`0=-5x+1\\\\5x=1\\\\x=(1)/(5)=0.2`

Then, we can graph the first line which passess through the points (0,1) and (0.2,0). Observe the graph attached.

The y-intercept of the second equation
`y=-2x-2` is:

`b=-2`

Now we need to find the x-intercept. Substitute
`y=0` and solve for "x":

`0=-2x-2\\\\2x=-2\\\\x=(-2)/(2)=-1`

Then, we can graph the second line, which passess through the points (0,-2) and (-1,0).

You can observe in the graph that the lines intersect at the point (1,-4). Therefore, that point is the solution of the system of equations.

Since the lines intersect, then there is one solution that is true for both equations. It is independent