How to solve 17x + 18y = 770?

17x + 18y = 770

There are an infinite number of solutions. Either in reals or integers.

An interesting problem is to find integer solutions.

17x + 18y = 770

770 = 45(17) + 5

18y = 17y + y

x = (770 - 18y) / 17

x = [45(17) + 5 - 17y - y] /17

x = 45 - y + (5-y)/17

One integral solution is

y=5, x=40

x=40, y=5

17(40) + 18(5) = 770

Other integral solutions trade off x and y values.

5-y = 17k

y = 5 -17k

x = 45 - (5-17k) + k

x = 40 + 18k

x = 40 + 18k, y = 5 - 17k

look for positive integers

k x y

0 40 5

-1 22 22

-2 4 39

That's all, folks!

You need to say what you want to solver for. It could be x or y.

17x + 18y = 770

Subtract 17x from each side

18y = -17x + 770

Divide by 18

y = -(17/18)x + 770/18

Reduce the fraction to lowest terms.

y = -(17/18)x + 385/9

That's the equation of a line in slope-intercept form.

Solving for x is similar.

With a calculator.

17x + 18y = 770

x=(770-18y)/17 .....y ∈ ℝ

you solve it by hanging yourself