hi, i'm having trouble understanding the concept of eliminating the parameter to obtain an equation in x and y alone. can anyone please solve this problem and explain it? thank you so much.
x = 3T-4
y= = 1-2T
(0<t<3) those signs are actually less than or equal to.
Solve each equation for T
from the first:
3T = x+4
T = (x+4)/3
from the second
2T = -y + 1
T = (-y+1)/2
but T=T
(x+4)/3 = (-y+1)/2
cross-multiply and simplify to get
2x+3y = -5
THANK YOU. i just really needed that bit of a start; now i can finish the rest. thanks again!
Of course, I can help you with that!
To eliminate the parameter, you need to eliminate the parameter variable (in this case, T) and express the equation solely in terms of x and y.
Let's solve the problem step by step:
We are given two equations:
x = 3T - 4 ...(1)
y = 1 - 2T ...(2)
First, let's solve equation (1) for T. Rearrange the equation to isolate T:
x = 3T - 4
4 + x = 3T
T = (4 + x)/3
Next, substitute this expression of T into equation (2):
y = 1 - 2T
y = 1 - 2((4 + x)/3)
Now, let's simplify equation (2) further:
y = 1 - (8 + 2x)/3
y = 1 - (8/3) - (2x/3)
y = 1 - 8/3 - 2x/3
y = -5/3 - 2x/3
Thus, by eliminating the parameter, we have the equation in terms of x and y alone:
y = -5/3 - 2x/3
Now, we have a linear equation where x and y are the variables.