Question 181781

3x - 2y = 5------eq1
5x + ay = 4 -----eq2
Put eq1 and eq2 in slope -intercept form (y=mx+b)
eq1:
-2y=5-3x  divide each side by -2
y=(3/2)x-5/2-------------------------eq1 in slope-intercept form
eq2:
ay=4-5x divide each side by a
y=(-5/a)x+4/a--------------------------eq2 in slope-intercept form

If eq1 and eq2 have the same slope, they are either parallel (no solutions) or lay on top of each other (infinite solutions), so:
(-5/a)=3/2  multiply each side by 2a
-10=3a a=-10/3
Substitute a=-10/3 into eq2:
y=(-5/(-10/3)x+4/(-10/3) simplify
y=(3/2)x-6/5  ------------------------------eq2a
Now if we compare eq1 and eq2a, we see that they have the same slope but not the same y-intercept which means that if a=-(10/3) the lines are parallel and there is no solution.

Hope this helps---ptaylor