Problem: (-3/10,-2) 10x-9y=15?
Show how to work the problem I know that this is the solution.
A single equation with two variables cannot be solved for a unique
value in either variable. It's true that the point you gave is a
solution, but it is only one of an infinite number of solutions.
Re-write the equation in slope-intercept form.
10x - 9y = 15
-9y = -10x + 15
y = 10/9 x - 15/9
y = 10/9 x - 5/3
Now, you can plug ANY value for x into the equation, and you will
get a corresponding value for y; every time. Put 3/2 in for x and
solve the equation.
10x - 9y = 15
10(3/2) - 9y = 15
15 - 9y = 15
15 - 9y - 15 = 15 - 15
-9y = 0
-9y/-9 = 0/-9
y = 0
So, (3/2, 0) is a solution.
Now, put -9 in for x.
10x - 9y = 15
10(-9) - 9y = 15
-90 - 9y = 15
-90 - 9y + 90 = 15 + 90
-9y = 105
-9y/-9 = 105/-9
y = -11 2/3
The fact is, you have the equation for a line. ANY point along that
line is a solution to the equation.