Prove the followingg statement: let a, b, c, m, n e z, where m 2 2 and n 2 2. if a b (mod m) and a c (mod n), then b c (mod d), where d = gcd(m, n). proof: for some n e z for some x e z. since a c (mod n), it follows that b (mod m), it follows that since a hence b-c= and since d gcd(m, n), it follows that for some e z and for some e z. therefore, b - c = | thus and so b c (mod d). since rx- sy e z, q. e.d

what is the answer?

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