Question 437138
3x -5y = -9
3x -6y = -8
Subtracting
y = -1
.
Substituting
3x -5(-1) = -9
3x +5 = -9
3x = -14
x = -14/3
.
Thus (-14/3, -1) appears to be the solution.
.
3(-14/3) - 5(-1) = ??
-14 +5 = -9  
Checks
.
3(-14/3) -6(-1) = ??
-14 +6 = -8
Checks
.
So, the solution (-14/3, -1) works for both equations.
.
We also can graph the equations to see if they cross at (-14/3, -1).
First, get these equations into slope-intercept.
.
3x -5y = -9
-5y = -3x -9
y = 3/5*x + 9/5
.
3x -6y = -8
-6y = -3x -8
y = 1/2*x + 4/3
.
{{{graph(500,500,-6,3,-6,3,3/5*x+9/5,1/2*x+4/3)}}}