help calculus?

x= 3-4t
4t = 3-x
t = (3-x)/4

y= 2-3t
3t = 2-y
t = (2-y)/3

t = (2-y)/3 = (3-x)/4
4(2-y) = 3(3-x)
8 - 4y = 9 - 3x
4y - 8 = 3x - 9

y = (3x-1)/4

The curve is a line with slope 3/4 and y-intercept -1/4

t = (2-y)/3
x = 3-(4/3)(2-y)
3x = 9-8+4y
3x - 4y = 1

x = 3 - 4t …… [1]
y = 2 - 3t …… [2]

From [1] :
4t = 3 - x
12t = 9 - 3x …… [3]

From [2] :
3t = 2 - y
12t = 8 - 4y …… [4]

[3] = [4] :
9 - 3x = 8 - 4y
3x - 4y - 1 = 0

The required Cartesian equation is : 3x - 4y - 1 = 0

4t = 3 - x
t = [ 3 - x ] / 4

y = 2 - [ 9 - 3x ] / 4
y = [ 8 - 9 + 3x ] / 4
y = [ 3x - 1 ] / 4

multiply the first equation by 3 and the second equation by 4, then subtract one of the resulting equations from the other

x=3-4t
4t=3-x
t=(3-x)/4

y=2-3t
3t = 2-y
t = (2-y)/3

(3-x)/4 = (2-y)/3
multiply both sides by 12
3(3-x )= 4(2-y)
9-3x = 8-4y
3x-4y = 1
-4y= 1-3x
4y= 3x-1
y = (3/4) x - 1/4

4t = 3 - x
t = (3 - x) / 4
&
3t = 2 - y
t = (2 - y) / 3
Hence eliminating 't'
(3 - x) / 4 = (2 - y) / 3
3(3 - x) = 4(2 - y)
9 - 3x = 8 - 4y
4y = 8 - 9 + 3x
4y = 3x - 1
y = 3x/4 - 1/4

12t = 3(3 - x) = 4(2 - y)
3x - 4y = 1 or if you prefer
y = (3/4)x - 1/4