Let us make the line from the picture, pointing the given equations:
From the draw and the given equations, we note that:
[tex]54=RT=RS+ST=4y+3+3y+9[/tex]
Therefore, we can solve the equation for y as follows
[tex]\begin{gathered} 54=4y+3+3y+9 \\ \\ 54=7y+12 \end{gathered}[/tex]
Where in the last line, we add the similar terms, for example 3y+4y=7y. Let us continue the calculations
[tex]\begin{gathered} 54=7y+12 \\ \\ 54-12=7y \\ \\ 42=7y \end{gathered}[/tex]
where in the second line of the equation above, we pass the 12 from the right to the left with opposite sign. We discover y as follows
[tex]\begin{gathered} 42=7y \\ \\ \frac{42}{7}=y \\ \\ 6=y \end{gathered}[/tex]
That is, we have y=6.
Let us now calculate the value of RD an RT. We know from the question that
[tex]\begin{gathered} RS=4y+3 \\ \\ ST=3y+9 \end{gathered}[/tex]
as we discover that y=6, substituting this value in the equations above we find:
[tex]\begin{gathered} RS=4\times\text{ }6+3=24+3=27 \\ \\ ST=3\times6+9=18+9=27 \end{gathered}[/tex]
We conclude that RS=27 and ST =27 .
