Step 1

(a) To find a system of two linear equations in the variables x and y whose solution set is given by the parametric equations

\(x = t\) and \(y = 3- 2t\)

solve y in term of x

\(y = 3-2x\)

\(2x + y =3\)

Step 2

b) To Find another parametric solution to the system in part (a) in which the parameter is s and y =s.

\(x=t...(1)\)

\(y=3-2t...(2)\)

\(y=s...(3)\)

To find t in terms of s

\(s=3-2t\)

\(\displaystyle{t}={\frac{{{3}-{s}}}{{{2}}}}\)

Therefore,

\(\displaystyle{x}={t}={\frac{{{3}-{s}}}{{{2}}}}\)

\(\displaystyle{x}={\frac{{{3}-{s}}}{{{2}}}}\)

\(y=s\)