103k views
3 votes
What is the x and the y and the z

What is the x and the y and the z-example-1
User Makboney
by
7.8k points

1 Answer

3 votes

x=2,\: z=3,\: y=-1

1) Let's solve this system. We can start by rewriting it this way:


\mleft\{\begin{matrix}3x-8y+z=17 \\ -x+y-z=-6 \\ x-3y=5\end{matrix}\mright.

Let's pick the 3rd equation and isolate x, from it:


x=5+3y

2) Now, we can plug that into the first and the 2nd equation.

Now let's solve this system to find y


\begin{gathered} \mleft\{\begin{bmatrix}3\mleft(5+3y\mright)-8y+z=17 \\ -\mleft(5+3y\mright)+y-z=-6\end{bmatrix}\mright? \\ 15+y+z=17 \\ -5-2y-z=-6 \\ ------------- \\ y=-z+2 \\ -5-2(-z+2)-z=-6 \\ -5+2z-4-z=-6 \\ z-9=-6 \\ z=9-6 \\ z=3 \end{gathered}

Now, let's find y based on y=-z+2 plug into that z=3


\begin{gathered} y=-3+2 \\ y=-1 \end{gathered}

2.2) And finally, let's find x


\begin{gathered} x=5+3y \\ x=5+3(-1) \\ x=5-3 \\ x=2 \end{gathered}

Hence, the answer is:


x=2,\: z=3,\: y=-1

User ZaTricky
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories