An object moves in the xy -plane. (parametric equations)

At time t, the position of the object is given by x = 9t − 5, y = 4t − 13. Determine when the object hits the x-axis. Then determine when the object his the y-axis.

A plot hits the x axis when y = 0

y = 4t - 13
0 = 4t - 13
4t = 13
t = 13/4 <===

A plot hits the y axis when x = 0

x = 9t - 5
0 = 9t - 5
9t = 5
t = 5/9 <===

x=9t-5
x+5=9t
(x+5)/9=t

y=4t-13
y+13=4t
(y+13)/4=t

t=t
(x+5)/9=(y+13)/4
4(x+5)=9(y+13)
4x+20=9y+117

when x=0, the object hits the y-axis
4(0)+20=9y+117
20-117=9y
-97=9y
-97/9=y

plug into
(y+13)/4=t
((-97/9)+13)/4=t
5/9=t
in unknown units

*edit
lol, oops
you can just set x=0 in the original equation for t

1/
y=0 ---> t = 13/4

2/
x=0--->t=5/9