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I am not the best at these I was hoping someone could help me.

I am not the best at these I was hoping someone could help me.-example-1

1 Answer

3 votes

Answer:


\begin{gathered} m=2 \\ YZ=25 \end{gathered}

Step-by-step explanation:

Given that Y is between X and Z;


XZ=XY+YZ

Given;


\begin{gathered} XZ=13m+6 \\ XY=9m-3 \\ YZ=6m+1 \end{gathered}

Let us substitute the given equation into the equation above;


\begin{gathered} XZ=XY+YZ \\ 13m+6=9m-3+6m+1 \\ 13m+6=9m+6m-3+1 \\ 13m+6=15m-2 \end{gathered}

Let now proceed to solve the equation;

add 2 to both sides of the equation;


\begin{gathered} 13m+6+2=15m-2+2 \\ 13m+8=15m \end{gathered}

subtract 13m from both sides;


\begin{gathered} 13m-13m+8=15m-13m \\ 8=2m \end{gathered}

Then lastly divide both sides by 2;


\begin{gathered} (8)/(2)=(2m)/(2) \\ 4=m \\ m=2 \end{gathered}

Since we have the value of m, let now substitute into YZ to get its value;


\begin{gathered} YZ=6m+1 \\ YZ=6(4)+1 \\ YZ=24+1 \\ YZ=25 \end{gathered}

Therefore, the value of m and YZ is;


\begin{gathered} m=2 \\ YZ=25 \end{gathered}

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