Explanation
Let's solve the 1st equation for variable y.
3x - 5y = 7
-5y = -3x+7
y = (-3x+7)/(-5)
y = (3/5)x - 7/5
Do the same for the other equation.
4y+11x = -5
4y = -11x-5
y = (-11x-5)/4
y = (-11/4)x - 5/4
Each result we arrived at is of the form y = mx+b
The first slope found was 3/5 while the second equation has slope -11/4.
Multiply these slopes to get: (3/5)*(-11/4) = -33/20 = -1.65
The result is not -1, so the lines are not perpendicular. Perpendicular slopes must multiply to -1 assuming neither line is vertical nor horizontal.
Put another way: If two lines are perpendicular, then one slope is the negative reciprocal of the other. For example, the slopes 2/3 and -3/2 are perpendicular.
