Question
upstudy study bank question image url

What is the \( x \)-value in the solution to this system of linear equations? \( \begin{array}{l}2 x-y=11 \\ x+3 y=-5 \\ -3 \\ -1 \\ 2 \\ 4\end{array} \)

Ask by Tucker Barnett. in the United States
Feb 19,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The \( x \)-value in the solution is 4.

Solution

Solve the system of equations \( 2x-y=11;x+3y=-5 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}2x-y=11\\x+3y=-5\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}y=-11+2x\\x+3y=-5\end{array}\right.\) - step2: Substitute the value of \(y:\) \(x+3\left(-11+2x\right)=-5\) - step3: Simplify: \(7x-33=-5\) - step4: Move the constant to the right side: \(7x=-5+33\) - step5: Add the numbers: \(7x=28\) - step6: Divide both sides: \(\frac{7x}{7}=\frac{28}{7}\) - step7: Divide the numbers: \(x=4\) - step8: Substitute the value of \(x:\) \(y=-11+2\times 4\) - step9: Calculate: \(y=-3\) - step10: Calculate: \(\left\{ \begin{array}{l}x=4\\y=-3\end{array}\right.\) - step11: Check the solution: \(\left\{ \begin{array}{l}x=4\\y=-3\end{array}\right.\) - step12: Rewrite: \(\left(x,y\right) = \left(4,-3\right)\) The solution to the system of linear equations is \( (x, y) = (4, -3) \). Therefore, the \( x \)-value in the solution is \( x = 4 \).

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

Extra Insights

To solve the system of equations, we'll use substitution or elimination. Let’s work with the equations \( 2x - y = 11 \) and \( x + 3y = -5 \). From the first equation, we can express \( y \) in terms of \( x \): 1. Rearranging gives us \( y = 2x - 11 \). 2. Substituting this expression for \( y \) into the second equation \( x + 3(2x - 11) = -5 \): \[ x + 6x - 33 = -5 \implies 7x - 33 = -5 \implies 7x = 28 \implies x = 4. \] Therefore, the \( x \)-value in the solution to this system of equations is \( 4 \). Now, let’s wrap up with some fun facts! The elimination method can be thought of like cooking; just like you combine ingredients to get a delicious dish, you combine equations to find an answer! And did you know? The concept of solving systems of equations dates back to Chinese mathematics in the 2nd century AD! It's fascinating how these techniques have evolved into the algebra we learn today.

Related Questions

Latest Algebra Questions

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