Kevin is 3 years older than daniel. Two years ago, Kevin was 4 times as old as Daniel. Let k be Kevin’s age and let d be Daniels age. What system of equations would represent this situation?

Daniel (now) is 3 years old,  (2 years ago) is 1 year old.

Kevin (now) is 6 years old,   (2 years ago) is 4 years old.

Step-by-step explanation:

Now:

-Kevin: k = d + 3

-Daniel: d

2 years ago:

-Kevin: k - 2 = 4(d - 2)

-Daniel: d - 2

We have the equation:

(k - 2) + 2 = k

4(d - 2) + 2 =  d + 3

4d - 8 + 2 = d + 3

3d - 6 = 3

3d = 9

d = 3

k = d + 3 = 3 + 3 = 6

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

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

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form