The two lines, p and q, are graphed below: line p is drawn by joining ordered pairs negative 8,15 and 6, negative 12. line q is drawn by joining ordered pairs 4,16 and negative 9,10 determine the solution and the reasoning that justifies the solution to the systems of equations. (0, 8), because this point is true for both the equations (0, 8), because the lines intersect the y-axis at these points (−2, 4), because this point makes both the equations incorrect (−2, 4), because it is the point of intersection of the two graphs

Solution:

Keep in mind ,

Equation of line joining two points (a,b) and (p,q) is given by :

Equation of line P which is obtained by  joining  (- 8,15) and (6, - 12) is given by:  

Equation of line Q which is obtained by  joining  (4,16) and (-9, 10) is given by:  

Equation of line P and Q are

27 x+14 y+6=0-------(1)× 2

6 x-13 y+184=0-------(2)× 9

54 x + 2 8 y+12=0---(1)

54 x -117 y +1656=0----(2)

(1) - (2)

145 y= 1644

y=11.33,

27 x+14 y+6=0-------(1)×13

6 x-13 y+184=0-------(1)×14

351 x + 182 y + 78=0-----(1)

84 x - 182 y +2576=0----(2)

(1) + (2)

435 x + 2654=0

x = - 6.11

So, solution set is (-6.11, 11.33)

Option (C) is true. (−2, 4), because this point makes both the equations incorrect.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3