SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given parametric equations
[tex]\begin{gathered} x=-3(t-2)---equation\text{ 1} \\ y=-3t------equation\text{ 2} \end{gathered}[/tex]
STEP 2: Rewrite equation 1
[tex]\begin{gathered} x=-3t+6 \\ -3t+6=x \end{gathered}[/tex]
STEP 3: Make t the subject of the equation
[tex]\begin{gathered} Subtract\text{ 6 from both sides} \\ -3t+6-6=x-6 \\ -3t=x-6 \\ Divide\text{ both sides by -3} \\ t=\frac{x-6}{-3} \\ t=\frac{-(x-6)}{3}=\frac{-x+6}{3} \end{gathered}[/tex]
STEP 4: Substitute the value of t above into equation 2 and solve in terms of x
[tex]\begin{gathered} y=-3t \\ By\text{ substitution,} \\ y=-3(\frac{-x+6}{3}) \\ Cross-cancel\text{ the common factor: 3} \\ y=-(-x+6) \\ y=x-6 \end{gathered}[/tex]
Hence, the answer in the simplest form solved for y is given as:
[tex]y=x-6[/tex]
