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2 years ago

Find the values of x and y if (-x + 5, 1) = (-y, 2x - 5y).

Mathematics

1 answer:

MrMuchimi2 years ago

7 0

Answer:

x = 8, y = 3

Step-by-step explanation:

Equating corresponding x and y coordinates , then

- y = - x + 5 ( multiply through by - 1 )

y = x - 5 → (1)

2x - 5y = 1 → (2)

Substitute y = x - 5 into (2)

2x - 5(x - 5) = 1 ← distribute and simplify left side

2x - 5x + 25 = 1

- 3x + 25 = 1 ( subtract 25 from both sides )

- 3x = - 24 ( divide both sides by - 3 )

x = 8

Substitute x = 8 into (1) for corresponding value of y

y = 8 - 5 = 3

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<u>Answer:</u>

The line equation that passes through the given points is 7x – y = 13

<u>Explanation:</u>

Given:

Two points are A(2, 1) and B(3, 8).

To find:

The line equation that passes through the given two points.

Solution:

We know that, general equation of a line passing through two points (x1, y1), (x2, y2) in point slope form is given by

$\frac{(y- y1)}{(x-x_1)}= \frac{((y_2- y_1)}{(x_2- x_1 )}$

${(y- y1)= \frac{((y_2- y_1)}{(x_2- x_1 )}\times(x-x_1)$ ..........(1)

here, in our problem x1 = 3, y1 = 8, x2 = 2 and y2 = 1.

Now substitute the values in (1)

$(y-8) = \frac{(1 - 8)}{(2 - 3)}\times(x- 3)$

$(y -8) = \frac{(- 7)}{(-1)}(x-3)$

y – 8 = 7(x – 3)

y – 8 = 7x – 21

7x – y = 21 – 8

7x – y = 13

Hence, the line equation that passes through the given points is 7x – y = 13

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