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Which one is the effiectentbway to solve substitution or elimination

The system of equations is:

\[
8x - y = -4
\]
\[
4x + 7y = -32
\]

To determine whether substitution or elimination is more efficient, let's quickly analyze both methods:

### Substitution
- You would first solve one of the equations for one variable, say \(y\) from the first equation:
  \[
  y = 8x + 4
  \]
  Then, substitute this expression into the second equation and solve for \(x\), followed by finding \(y\).

### Elimination
- To eliminate one variable, you would need to make the coefficients of either \(x\) or \(y\) the same in both equations. Here, multiplying the second equation by 2 gives:
  \[
  8x + 14y = -64
  \]
  Now subtract the first equation from this new equation to eliminate \(x\), solving for \(y\), and then finding \(x\).

### More Efficient Method
In this case, **elimination** seems more efficient because you can quickly eliminate \(x\) without dealing with fractions. Substitution would introduce a more complicated expression, which could make solving more tedious.

Would you like me to proceed with elimination to find the solution, or do you prefer another method?

Let me know if you have any questions! Meanwhile, here are 5 related questions:
1. What are the general steps for solving systems of equations by elimination?
2. How would substitution introduce fractions in this case?
3. When is substitution typically more efficient than elimination?
4. How do you interpret the solution of a system of equations geometrically?
5. Can systems of equations have no solution or infinitely many solutions?

**Tip**: When coefficients of one variable are easy to equalize, elimination tends to be faster.

Which one is the efficient way to solve: substitution or elimination?

Learn how to determine the most efficient method to solve the system of equations 8x - y = -4 and 4x + 7y = -32. This problem focuses on the comparison between elimination and substitution methods, with detailed analysis and solution steps. Suitable for students in Grades 9-11.

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