Use a separate sheet of paper to solve the system of inequalities by graphing. Use the graph to decide if the point (-3. 2) is part of the solution set to the system. Explain your answer in the box provided below
y<-4-3
x+8y>7

  The point is part of the solution. It is found in the doubly-shaded area.

Step-by-step explanation:

The first inequality graphs with a solid boundary line of negative slope that has negative x- and y-intercepts. Shading is below the line (and to its left).

The second inequality graphs with a solid boundary line of negative slope that has positive x- and y-intercepts. Shading is above the line.

The solution space is the doubly-shaded area to the (upper) left of the point where the boundary lines cross. The given point is in the 2nd quadrant, and is in the solution space.

The point is part of the solution set.

__

Additional comment

Sometimes help is needed with graphing.

If a variable in the inequality has a coefficient of 1, its corresponding intercept is easily found. (It is the constant on the other side of the inequality symbol.)

The slope of the boundary line can be found by solving for y. The slope is the coefficient of x in that formulation. For the first inequality, the slope is -4 and the y-intercept is -3. This means (-1, 1) and (-2, 5) will be other points on the line.

For the second inequality, the slope is -1/8, and the x-intercept is 7. This, too, means that (-1, 1) is a point on the line, along with (-9, 2).

Slope is rise/run. A slope of -1/8 means the line falls 1 unit (rise) for each 8 units to the right (run). Working the other direction, the line will rise 1 unit for each 8 units to the left.

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this