# (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.

Equations

(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 $$y =s.$$

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