Question

The graph plots four equations, A, B, C, and D: Line A joins ordered pair negative 6, 16 and 9, negative 4. Line B joins ordered pair negative 2, 20 and 8, 0. Line C joins ordered pair negative 7, negative 6 and 6, 20. Line D joins ordered pair 7, 20 and 0, negative 7. Which pair of equations has (4, 8) as its solution?
Equation A and Equation C
Equation B and Equation C
Equation C and Equation D
Equation B and Equation D'

Answer 1

Answer:

Option D : Equation B and Equation D.

Step-by-step explanation:

We are given that four equations A,B,C and D

The equation of a line which passing through the two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by

$\frac{y-y_1}{y_1-y_2}=\frac{x-x_1}{x_1-x_2}$

Using this formula we obtain the equation of line A ,B,C and D

The line A which passing through the points (-6,16) and (9,-4) is given by

$\frac{y-16}{16+4}=\frac{x+6}{-6-9}$

Where $x_1=-6,y_1=16,x_2=9,y_2-4$

The equation of line A is given by

$\frac{y-16}{20}=\frac{x+6}{-15}$

The equation of line A is given by

$\frac{y-16}{4}=-\frac{x+6}{3}$

Denominator on both side divided by 5

The equation of line A is given by

$3y-48=-4x-24$

The equation of line A is given by

$4x+3y=-24+48$

The equation of  line A is given by

$4x+3y=24$

The equation of line B which passing through the points (-2,20) and (8,0) is given by

$\frac{y-20}{20-0}=\frac{x+2}{-2-8}$

Where $x_1=-2,y_1=20,x_2=8,y_2=0$

The equation of line B is given by

$\frac{y-20}=-2(x+2)$

The equation of line B is given by

$y-20=-2x-4$

The equation of line B is given by

$2x+y=-4+20=16$

The equation of a line B which passing through the points (-2,20) and (8,0) is given by

$2x+y=16$

The equation of line C which passing through the points (-7,-6) and (6,20) is given by

$\frac{y+6}{-6-20}=\frac{x+7}{-7-6}$

where$x_1=-7,y_1=-6,x_2=6,y_2=20$

The equation of a line C is given by

$y+6=2(x+7)$

The equation of a line C is given by

$2x-y=6-7=-1$

The equation of line C which passing through the points (-7,-6) and (6,20) is given by

$2x-y=-1$

The equation of a line D which passing through the points (7,20) and (0,-7) is given by

$\frac{y-20}{20+7}=\frac{x-7}{7-0}$

Where $x_1=7,y_1=20,x_2=0,y_2=-7$

The equation of a line D is given by

$\frac{y-20}{27}=\frac{x-7}{7}$

The equation of line D is given by

$7y-140=27x-189$

Using cross multiply method

The equation of a line D is given by

$27x-7y=189-140=49$

The equation of a line D which passing through the points (7,20) and (0.-7) is given by

$27x-7y=49$

From graph we can see line B and D are intersect at point (4,8).Therefore, the solution of equation B and equation D is (4,8).

Hence, option D is correct.

Answer 2

Equation C & D is the only possible answers.