Question

Graph the system below and write its solution.

y = -1/2 x -1

-2 + y = -6

.. there is also "no solution" or "infinite solution" answers.

Answer 1

See the graph attached. It has one solution: (6,-4)

Explanation:

The slope-intercept form of a line is:

`y=mx+b`

Where m is the slope and b is the intersection of the line with the y-axis.

Given the first equation
`y =(-1)/(2)x -1`

You can identify that:

b=-1

Substitute y=0 to find the intersection with the x-axis

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

This line passes through the points (0,-1) and (-2,0)

Given the second equation:

`-2 + y = -6`

Solve for y:

`y = -6+2\\y=-4`

It passes through the point (0,-4).

Now, you can graph. See the figure attached.

It has one solution,which is the point of intersection of both lines: (6,-4)