Question

Find 4 solutions for 3x-5y+30=0

Answer 1

Answer:

x = -10, y = 0

x = -5, y = 3

x = 0, y = 6

x = 5, y = 9

Step-by-step explanation:

Since 30 = 3 × 10, one obvious solution is

x = -10, y = 0

Since 30 = 5 × 6, another obvious solution is

x = 0, y = 6

For other solutions, notice that if 3x-5y+30=0, then

3(x+5) - 5(y+3) + 30  =  3x + 15 - 5y - 15 + 30 = 3x - 5y + 30 = 0.

So if x,y is one solution, then x+5,y+3 is another solution.

Therefore, starting with x = -10, y = 0, we get a whole heap of other solutions by increasing x by 5 and y by 3:

x = -5, y = 3

x = 0, y = 6  (already got this one above)

x = 5, y = 9

x = 10, y = 12

etc.