y≥−3x−7 y, is less than, x, plus, 5 y<x+5

Answer 1

if

y>/= -3x

and

y< x+5

graph them both to see what values of x and y satisfy both

y=-3x-7 is a boundary of the first constraint, so make it with a solid line, downward sloping with slope =-3 with y intercept = -7, the inequality sign > means shade in the area above that line

y< x+5 is the area below the line y=x+5, a straight line with slope = 1, and through the y intercept = 5

make the line dotted, as the inequality does not include those points on the line

now look where the two shaded areas overlap, that's the solution set of (x,y) values that satisfy both inequalities, also put arrows pointing to the right of that overlapped shaded area to indicate the (x,y) values go infinitely to to the right

the two lines intersect where x+5=-3x-7,

where 4x =-12, x=-3, y= 2, or at the point (-3,2)

the solution set is mostly in quadrants I and IV, but also some points in II and III,

a small triangular area in quadrant III with vertices (-7/3,0), (0,-7) and (0,0),

and a small quadrilateral area in quadrant II with vertices (-7/3,0), (-3,2), (0,5) and (0,0)

the two given inequalities describe the solution set

use a graphing calculator or plot the points and lines above to visually see the solution set