Beck Long
04/17/2024 · High School
2. Resuelva el siguiente sistcma ntilizando el método de igualación: \[ \left\{\begin{array}{l}3 x+y=7 \\ 2 x-y=3\end{array}\right. \]
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Solve the system of equations \( 3x+y=7; 2x-y=3 \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}3x+y=7\\2x-y=3\end{array}\right.\)
- step1: Solve the equation:
\(\left\{ \begin{array}{l}y=7-3x\\2x-y=3\end{array}\right.\)
- step2: Substitute the value of \(y:\)
\(2x-\left(7-3x\right)=3\)
- step3: Simplify:
\(5x-7=3\)
- step4: Move the constant to the right side:
\(5x=3+7\)
- step5: Add the numbers:
\(5x=10\)
- step6: Divide both sides:
\(\frac{5x}{5}=\frac{10}{5}\)
- step7: Divide the numbers:
\(x=2\)
- step8: Substitute the value of \(x:\)
\(y=7-3\times 2\)
- step9: Simplify:
\(y=1\)
- step10: Calculate:
\(\left\{ \begin{array}{l}x=2\\y=1\end{array}\right.\)
- step11: Check the solution:
\(\left\{ \begin{array}{l}x=2\\y=1\end{array}\right.\)
- step12: Rewrite:
\(\left(x,y\right) = \left(2,1\right)\)
El sistema de ecuaciones se resuelve utilizando el método de igualación y se obtiene la solución: \( (x,y) = (2,1) \).
Quick Answer
La solución del sistema es \( (x,y) = (2,1) \).
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit