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

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,

From the question

x₁ = -7

y₁ = -4

x₂ = 14

y₂ = 2

Putting these values into the equation,

We get

∴

This becomes,

Clearing the brackets

Then,

Dividing through by 3

We get

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

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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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=141

14A+2B=142

-14A+-8B=283

14A+2B=142

0-6B=42

6B=42

B=42/6

B=7

put B=7 in eqn 1 we have

-7A-4(7)=141

-7A-28=14

-7A=14+28

-7A=42

A=42/-7

A=-6

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answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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