#6 i Solve the system by substitution. x = 2y +2 !! 2х - 5у%3D1 The solution is

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
icon
Related questions
Question

Can you help me with this question?

**Problem #6: Solving a System by Substitution**

To solve the system of equations using substitution, follow these steps:

1. **Equations Given:**
   \[
   x = 2y + 2
   \]
   \[
   2x - 5y = 1
   \]

2. **Substitute the Expression:**
   Substitute \( x = 2y + 2 \) into the second equation:
   \[
   2(2y + 2) - 5y = 1
   \]

3. **Solve for \( y \):**
   \[
   4y + 4 - 5y = 1
   \]
   \[
   -y + 4 = 1
   \]
   \[
   -y = 1 - 4
   \]
   \[
   -y = -3
   \]
   \[
   y = 3
   \]

4. **Find \( x \):**
   Substitute \( y = 3 \) back into the expression for \( x \):
   \[
   x = 2(3) + 2
   \]
   \[
   x = 6 + 2
   \]
   \[
   x = 8
   \]

5. **Solution:**
   The solution to the system of equations is \((8, 3)\).

**The Solution is \((8, 3)\)**

Use the substitution method carefully to find the values of \( x \) and \( y \) that satisfy both equations. Check the solution by plugging back into the original equations.
Transcribed Image Text:**Problem #6: Solving a System by Substitution** To solve the system of equations using substitution, follow these steps: 1. **Equations Given:** \[ x = 2y + 2 \] \[ 2x - 5y = 1 \] 2. **Substitute the Expression:** Substitute \( x = 2y + 2 \) into the second equation: \[ 2(2y + 2) - 5y = 1 \] 3. **Solve for \( y \):** \[ 4y + 4 - 5y = 1 \] \[ -y + 4 = 1 \] \[ -y = 1 - 4 \] \[ -y = -3 \] \[ y = 3 \] 4. **Find \( x \):** Substitute \( y = 3 \) back into the expression for \( x \): \[ x = 2(3) + 2 \] \[ x = 6 + 2 \] \[ x = 8 \] 5. **Solution:** The solution to the system of equations is \((8, 3)\). **The Solution is \((8, 3)\)** Use the substitution method carefully to find the values of \( x \) and \( y \) that satisfy both equations. Check the solution by plugging back into the original equations.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education