Question

The points that satisfy the system $x+y=1,x^2+y^2<25$, where the symbol "<" means "less than," constitute the following set:

• A. only two points
• B. an arc of a circle
• C. a straight line segment not including the end points
• D. a straight line segment including the end points
• E. a single point

Answer 1

The correct option is C a straight line segment not including the end points

x+y=1 denotes a line, whereas x^2+y^2<25 denotes region inside a circle with centre (0,0) and radius 5 not including the points on the circle. So system satisfying these 2 conditions will contain points on the line x+y=1 inside the circle excluding the two points of intersection.