The rule for the number of fish in a home aquarium is 1 gallon of water for each inch of fish length. marta’s aquarium holds 31 gallons of water and hank’s aquarium hold 41 gallons of water. the aquarium holds two types of fish, fish a of fish b. if marta bought 3 of fish a and 2 of fish b, and hank bought 3 of fish a and 4 of fish b, how long is fish a and how long is fish b

fish a is 7 inches long

fish b is 5 inches long

Step-by-step explanation:

set up system of equations and use subtraction

Marta's    3a + 2b = 31

Hank's .   3a + 4b = 41

subtract the two equation (make sure you take the negative all the way through the bottom equation

3a cancels with -3a and you are left with

-2b = -10

b = 5

plug b = 5 into one of the equations and solve for a.

a

step-by-step explanation:

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