Question

(a) 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.

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asked 2021-02-14

(a) 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 \(= 3- 2t.\)
(b) Find another parametric solution to the system in part (a) in which the parameter is s and \(y =s.\)

Answers (1)

2021-02-16

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

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