Find a parametric representation of the solution set of the linear equation.

gabioskay7

gabioskay7

Answered question

2021-11-16

Find a parametric representation of the solution set of the linear equation.
3x − 1/2y = 9

Answer & Explanation

hotcoal3z

hotcoal3z

Beginner2021-11-17Added 16 answers

Step 1
Given equation is
3x12y=9...(1)
Where x and y are unknown.
Step 2
Since equation (1) is a single equation in two unknowns, so equation has infinitely many solution.
Let
x=t (some scalar)
Put in equation (1)
3t12y=9
3t9=12y
y=6t-18
Step 3
Hence solution set of given equation is
[xy]=[t6t18]
=t[16]+[018]

John Twitchell

John Twitchell

Beginner2021-11-18Added 19 answers

Calculation:
Consider 3x12y=9.
Choosing y to be a free variable, solve for x in terms of y.
3x12y=9
6xy2=9
6x-y=9*2
6x-y=18
6x=18+y
x=18+y6
=186+16y
x=3+16y
Letting y=t, we obtain the parametric representation as x=3+16t, y=t where t is any real number.
Thus the parametric representation of the solution set is {x,y}={3+16t,t} where t is any real number.

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