Question

1. 2x-y=0

Answer 1

Answer:

(1) $(x,y) = (-2,-4)$

(2) $y = 4x -26$

(3) $x = 1$

Step-by-step explanation:

(1):

$2x - y = 0$

$x + 3y = -14$

Required: Solve for x and y

Make x the subject in $x + 3y = -14$

$x = -3y - 14$

Substitute -3y - 14 for x in the first equation

$2x - y = 0$

$2(-3y-14) - y = 0$

Open bracket

$-6y - 28 - y = 0$

Collect Like Terms

$- y-6y = 28$

$-7y = 28$

Divide both sides by -7

$y = -4$

Substitute -4 for y in $2x - y = 0$

$2x - (-4) = 0$

$2x + 4 = 0$

Collect Like Terms

$2x = -4$

Divide by 2

$x = -2$

Hence, the solution is:

$(x,y) = (-2,-4)$

(2):

$(x_1,y_1) = (7,2)$ -- points

$m = 4$ --- slope

Required: Determine the line equation

This is calculated using:

$y = m(x - x_1) + y_1$

This gives:

$y = 4(x - 7) + 2$

Open bracket

$y = 4x - 28 + 2$

$y = 4x -26$

(3)

$4 - 5x + 3 = 4x - 2$

Required: Solve for x

Collect Like Terms

$- 5x -4x = - 2-3-4$

$-9x = -9$

Divide both sides by -9

$x = 1$