Question
upstudy study bank question image url

\( \rightarrow \begin{array} { r } { - 2 x - 3 y + z = - 9 } \\ { - 2 x + y - 3 z = 7 } \\ { x - y + 2 z = - 5 } \end{array} \} \)

Ask by Salazar Barrett. in Indonesia
Jan 24,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

The system of equations has no solution.

Solution

Solve the system of equations \( -2x-3y+z=-9;-2x+y-3z=7;x-y+2z=-5 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}-2x-3y+z=-9\\-2x+y-3z=7\\x-y+2z=-5\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}z=-9+2x+3y\\-2x+y-3z=7\\x-y+2z=-5\end{array}\right.\) - step2: Substitute the value of \(z:\) \(\left\{ \begin{array}{l}-2x+y-3\left(-9+2x+3y\right)=7\\x-y+2\left(-9+2x+3y\right)=-5\end{array}\right.\) - step3: Simplify: \(\left\{ \begin{array}{l}-8x-8y+27=7\\5x+5y-18=-5\end{array}\right.\) - step4: Solve the equation: \(\left\{ \begin{array}{l}x=\frac{5-2y}{2}\\5x+5y-18=-5\end{array}\right.\) - step5: Substitute the value of \(x:\) \(5\times \frac{5-2y}{2}+5y-18=-5\) - step6: Simplify: \(\frac{5\left(5-2y\right)}{2}+5y-18=-5\) - step7: Multiply both sides of the equation by LCD: \(\left(\frac{5\left(5-2y\right)}{2}+5y-18\right)\times 2=-5\times 2\) - step8: Simplify the equation: \(-11=-10\) - step9: The statement is false: \(y \in \varnothing \) - step10: Calculate: \(\left\{ \begin{array}{l}x \in \varnothing \\y \in \varnothing \\z \in \varnothing \end{array}\right.\) - step11: Rewrite: \((x, y, z) \in \varnothing\) The system of equations has no solution.

Reviewed and approved by the UpStudy tutoring team

error msg
Explain
Simplify this solution

Bonus Knowledge

Let's dive into some fascinating elements related to solving systems of equations! The method of substitution or elimination are two common techniques used to solve systems of equations like the one you've presented. Each method can bring unique insights into the relationships between the variables, and can often make complex solutions feel straightforward. With practice, transforming the equations to find the values of \(x\), \(y\), and \(z\) can become as easy as pie! When tackling these systems, be mindful of common pitfalls, such as losing track of signs or misreading equations. A classic mistake is combining terms incorrectly or forgetting to apply operations consistently across the entire equation. Always double-check your work and consider plugging your solution back into the original equations to confirm that they hold true!

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy