Question

1. 2x-y=0

X+3y=-14


2. Write the equation of the line in slope intercept form that goes through the point (7,2) and has a slope of 4.

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

Show steps, thx:)

Answer 1

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

(2)
`y = 4x -26`

(3)
`x = 1`

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`