Question

Which part of the graph best represents the solution set to the system of inequalities y<_ x+1 and y+x<_ -1

Answer 1

Hello!

Remember that the symbols: ≤ and ≥ are graphed as a solid line. While the symbols: < and > are graphed as a dotted line.

Also, before graphing, it would be better to convert both equations to slope-intercept form.

y ≤ x + 1 is already in slope-intercept form.

y + x ≤ -1 is not written in slope-intercept form. (Slope-intercept form: y = mx + b)

y + x ≤ - 1 (subtract x from both sides)

y ≤ -x - 1

Graphing those lines, you get the graph below. You can see that Part C best represents the solution set systems of inequalities, because that is where both of the shaded lines intersect.

Answer: Part C

Answer 2

Hence, the solution set of the graph of the system of linear inequalities lies in:

PART C

Explanation:

We are asked to find which part of the graph represents the solution set of the system of equations:

y ≤ x+1 This inequality could also be written as:

-x+y ≤ 1 ( The graph of this inequality will be a straight line passing through (-1,0) and (0,1) with shading lying towards the origin)

y+x ≤ -1 ( The graph of this inequality will be a straight line passing through (-1,0) and (0,-1) and shaded region away the origin)

Hence, the shaded region of the solution will lie in:

PART C