Answer:
[tex]\begin{gathered} m=2 \\ YZ=25 \end{gathered}[/tex]
Explanation:
Given that Y is between X and Z;
[tex]XZ=XY+YZ[/tex]
Given;
[tex]\begin{gathered} XZ=13m+6 \\ XY=9m-3 \\ YZ=6m+1 \end{gathered}[/tex]
Let us substitute the given equation into the equation above;
[tex]\begin{gathered} XZ=XY+YZ \\ 13m+6=9m-3+6m+1 \\ 13m+6=9m+6m-3+1 \\ 13m+6=15m-2 \end{gathered}[/tex]
Let now proceed to solve the equation;
add 2 to both sides of the equation;
[tex]\begin{gathered} 13m+6+2=15m-2+2 \\ 13m+8=15m \end{gathered}[/tex]
subtract 13m from both sides;
[tex]\begin{gathered} 13m-13m+8=15m-13m \\ 8=2m \end{gathered}[/tex]
Then lastly divide both sides by 2;
[tex]\begin{gathered} \frac{8}{2}=\frac{2m}{2} \\ 4=m \\ m=2 \end{gathered}[/tex]
Since we have the value of m, let now substitute into YZ to get its value;
[tex]\begin{gathered} YZ=6m+1 \\ YZ=6(4)+1 \\ YZ=24+1 \\ YZ=25 \end{gathered}[/tex]
Therefore, the value of m and YZ is;
[tex]\begin{gathered} m=2 \\ YZ=25 \end{gathered}[/tex]
