system of equations

Question

Consider the following system of equation: 3𝑥 − 4𝑦 = 0 and 4𝑥 − 5𝑦 = 𝑘 where k is a constant Real Number. Solve the system for (x,y) in terms of k. Do not replace the constant k with a numerical value. Give your solution as an ordered pair in terms of k

Answer 1

3x-4y=0

4x-5y= k

12x-15y= 3k is 2nd equation times 3

12x -16y= 0 is 1st equation times 4

subtract the new equations

-15y - (-16y)=3k-0

16y-15y= 3k-0

y=3k

x=4y/3= 4(3k)/3= 4k

solution = (4k, 3k)