7x+y=-3.   4x-y=14 solve usin substitution 

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

1. **Rewrite one of the equations to express one variable in terms of the other.**

   Let's take the second equation and solve for \( y \):

   \[
   4x - y = 14
   \]

   Add \( y \) to both sides:

   \[
   4x = y + 14
   \]

   Subtract 14 from both sides to solve for \( y \):

   \[
   y = 4x - 14
   \]

2. **Substitute this expression into the first equation.**

   Now, substitute \( y = 4x - 14 \) into the first equation:

   \[
   7x + y = -3
   \]

   Replace \( y \) with \( 4x - 14 \):

   \[
   7x + (4x - 14) = -3
   \]

3. **Simplify and solve for \( x \).**

   Combine like terms:

   \[
   7x + 4x - 14 = -3
   \]

   \[
   11x - 14 = -3
   \]

   Add 14 to both sides:

   \[
   11x = 11
   \]

   Divide by 11:

   \[
   x = 1
   \]

4. **Substitute \( x \) back into the expression for \( y \).**

   Use \( x = 1 \) in the expression \( y = 4x - 14 \):

   \[
   y = 4(1) - 14
   \]

   Simplify:

   \[
   y = 4 - 14
   \]

   \[
   y = -10
   \]

So, the solution to the system of equations is \( x = 1 \) and \( y = -10 \).

### Solution:
\[
x = 1, \quad y = -10
\]

Would you like more details or have any questions about this solution?

### Related Questions:
1. Can you show how to solve the system using the elimination method?
2. How can we verify the solution \( x = 1 \) and \( y = -10 \)?
3. What would the graph of these two equations look like?
4. How do substitution and elimination methods compare in terms of efficiency?
5. How can we set up a system of equations from a word problem?
6. What are the steps for solving a system of equations with three variables?
7. How can we identify if a system of equations has no solution or infinitely many solutions?
8. What are some real-life applications of solving systems of equations?

### Tip:
When solving systems of equations, keep your work organized and clearly write each step to avoid mistakes.

Learn how to solve the system of equations 7x + y = -3 and 4x - y = 14 using the substitution method. Detailed step-by-step solution provided, covering algebraic concepts and the substitution method. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation