i only have just one question please someone actually help me with my homework please

Question

Identify the graph that represents the given system of inequalities and the classification of the figure created by the solution region.

A.) triangle

B.) quadrilateral

C.) triangle

D.) quadrilateral

Please just give and only give explanation and solution.

Answer 1

Well the second inequality is the easiest...

it is a SOLID VERTICAL line at x=-1, shades to the right;

so options B, C and D are ELIMINATED...

Next,

solves the first inequality for y:

3x + y <= 2

y <= -3x + 2

this is a SOLID line, with y-intercept at (0,2);

the slope is -3, so the next point (down 3, 1 to the right)

is at (1,-1); [adds 1 to x and subtracts 3 from y];

then next point is then (2,-4);

Testing the origin (x=0,y=0); 0 <= -3(0) + 2 --> 0 < 2 is true,

so shades TOWARDS the origin;

The last inequality , when solved for y is y >= (1/2)x - 2

the y-intercept is (0,-2) with slope 1/2

Testing the origin, 0 >=-2 is true, so shades towards the origin

option A better fits these descriptions...