Question
upstudy study bank question image url

7 Solve the given linear system of equations: \( 5 x+3 y=-9 \) \( -10 x-9 y=-3 \) \( y=\square \) Question Help: \( \square \) Message instructor

Ask by Howell Dickson. in Canada
Mar 14,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

\( y = 7 \)

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Mind Expander

To solve the system of equations, we can use the method of substitution or elimination. Let's use elimination for this example. First, we can manipulate the first equation \(5x + 3y = -9\) by multiplying it by 2, to align it with the second equation which has coefficients suitable for elimination: \[ 2(5x + 3y) = 2(-9) \implies 10x + 6y = -18 \] Now we have: 1. \(10x + 6y = -18\) 2. \(-10x - 9y = -3\) Next, we can add both equations: \[ (10x - 10x) + (6y - 9y) = -18 - 3 \] This simplifies to: \[ -3y = -21 \] Thus, solving for \(y\): \[ y = 7 \] Now, substitute \(y = 7\) back into the first equation to solve for \(x\): \[ 5x + 3(7) = -9 \] \[ 5x + 21 = -9 \] \[ 5x = -30 \implies x = -6 \] So, the solution to the system of equations is \(x = -6\) and \(y = 7\). The final answer is: \(y = 7\)

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