Please help, I need an explanation on how to do this type of problems. I've been at this assignment for the whole day and I'm nearing the end of it but my teacher hasn't taught this level of difficulty for this concept and expects us to reach 100 score.

See image

Step-by-step explanation:

To graph the inequality

-2x + y >= -10

Change it to y = mx + b form, use a solid line (bc of the "or equal to" underline)

y >= 2x - 10 We have y-intercept at -10 and slope 2/1, shading goes above the line.

The other graph is an absolute value graph; it has a v-shape. The 7 makes it stretched 7 times taller (and skinnier) the -4 by the x shifts the whole graph to the right 4 units. The -4 at the end of the equation shifts the whole graph down 4 units. See image. The shading goes above the V (kind of looks like inside)

The solution to the system is where the shading of the two overlap. It is mostly the shading for the absolute value graph except for a tiny triangle at the bottom. See image.