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

Equation C & D is the only possible answers.

Answer 2

Option D : Equation B and Equation D.

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

`(y-y_1)/(y_1-y_2)=(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

`(y-16)/(16+4)=(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

`(y-16)/(20)=(x+6)/(-15)`

The equation of line A is given by

`(y-16)/(4)=-(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

`(y-20)/(20-0)=(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

`(y+6)/(-6-20)=(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

`(y-20)/(20+7)=(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

`(y-20)/(27)=(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.