Question

Can someone please solve this, i need it quickly

Answer 1

3x + y = 20 and x - 2y = - 4

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

(a)

Given

3x + y = 17 ( subtract 3x from both sides )

y = - 3x + 17 ← in slope- intercept form

with slope m = - 3

Para;;el lines have equal slopes , then

y = - 3x + c ← is the partial equation

To find c substitute (4, 8) into the partial equation

8 = - 12 + c ⇒ c = 8 + 12 = 20

y = - 3x + 20 ← in slope- intercept form

Add 3x to both sides

3x + y = 20 ← in standard form

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(b)

Given

y + 2x = 13 ( subtract 2x from both sides )

y = - 2x + 13 ← in slope- intercept form

with slope m = - 2

Given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-2)` =
`(1)/(2)` , then

y =
`(1)/(2)` x + c ← is the partial equation

To find c substitute (2, 3) into the partial equation

3 = 1 + c ⇒ c = 3 - 1 = 2

y =
`(1)/(2)` x + 2 ← in slope- intercept form

Multiply through by 2 to clear the fraction

2y = x + 4

x - 2y = - 4 ← in standard form