Graph the system below and write its solution. y= -1/2x-1 and -2x+y= -6

Question

I need help solving this.. Thanks!

Answer 1

It's going to be hard to graph without graph paper, but I'll try and tell you what to do.

When an equation is set up as y=mx+b, the m is the slope and the b is the y-intercept. That means the number at the end is where the line crosses the y-axis, and the number before the x is how much you go up and over.

So, for your first equation (y=-1/2x-1), the line crosses the y-axis at -1, so put a point at (0,-1). From there, you count down 1 and to the right 2 and put another point -- because a slope of -1/2 means go down one and over two). So your next point should be at (-1, 1). Now you can draw a line connecting those two points (and going beyond them.

Your second equation needs to be set up like the first one, so you have it in y=mx+b format. So first you need to add 2x to both sides in order to move the -2x.

Now you have y=2x-6. Using the same process, the y-intercept for this line is at (0,-6). The slope is 2, which is the same as 2/1. (Any whole number can be turned into a fraction by putting it over 1). So you go up 2 and over 1 (positive slope goes up; negative slope goes down). Your next point should be at (2,-5).

Once you've drawn your two lines, the point where they cross each other is the solution to the system.