Question

The equation Ax + By = 14 goes through the coordinates (-7, -4) and (14, 2).
What are the values of A and B?

Answer 1

Answer:

A=-6

B=7

Step-by-step explanation:

We want to solve for the values of A and B.

let us substitute the values of the coordinates, that is x and y into the expression and obtain the two equations.

then we solve simultaneously

-7A-4B=14---------1

14A+2B=14--------2

-14A+-8B=28---------3

14A+2B=14------------2

0-6B=42

6B=42

B=42/6

B=7

put B=7 in eqn 1 we have

-7A-4(7)=14---------1

-7A-28=14

-7A=14+28

-7A=42

A=42/-7

A=-6

Answer 2

The values of A and B are 3 and -7 respectively

In order to determine the values of A and B,

First, we will determine the equation of the line passing through the coordinates (-7, -4) and (14, 2).

Using the formula for determining the equation of a line with two given points,

$\frac{y-y_{1} }{x -x_{1} } =\frac{y_{2}-y_{1} }{x_{2}-x_{1}}$

From the question

x₁ = -7

y₁ = -4

x₂ = 14

y₂ = 2

Putting these values into the equation,

We get

$\frac{y--4}{x--7} =\frac{2--4}{14--7}$

∴ $\frac{y+4}{x+7} =\frac{2+4}{14+7}$

$\frac{y+4}{x+7} =\frac{6}{21}$

This becomes,

$6(x+7) = 21(y+4)$

Clearing the brackets

$6x + 42 = 21y + 84$

Then,

$6x -21y = 84 -42$

$6x -21y = 42$

Dividing through by 3

We get

$3x - 7y = 14$

∴ The equation of the line that goes through the coordinates (-7, -4) and (14, 2) is $3x - 7y = 14$

Now, we will compare the above equation to the equation given.

The given equation is Ax + By = 14

By comparing

A = 3 and B = -7

Hence, the values of A and B are 3 and -7 respectively

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