solve each system by elimination

4x - 3y = -2
4x + 5y = 14

To solve the system of equations by elimination, we want to eliminate one variable. Here are the steps:

### System of equations:
1. \( 4x - 3y = -2 \)
2. \( 4x + 5y = 14 \)

### Step 1: Eliminate \(x\)
Both equations have the same \(4x\), so we can subtract one equation from the other to eliminate \(x\).

Subtract equation 1 from equation 2:
\[
(4x + 5y) - (4x - 3y) = 14 - (-2)
\]
\[
4x + 5y - 4x + 3y = 14 + 2
\]
\[
8y = 16
\]

### Step 2: Solve for \(y\)
\[
y = \frac{16}{8} = 2
\]

### Step 3: Substitute \(y = 2\) into one of the original equations
Substitute \(y = 2\) into equation 1:
\[
4x - 3(2) = -2
\]
\[
4x - 6 = -2
\]
\[
4x = 4
\]
\[
x = 1
\]

### Solution:
The solution to the system is \(x = 1\) and \(y = 2\).

Would you like further details on any step or have any questions?

Here are 5 related questions:
1. How do you solve a system using substitution instead of elimination?
2. Can this system be solved graphically? What does the graph look like?
3. What happens if both equations have the same coefficients for \(y\) instead of \(x\)?
4. Can you explain how to check the solution by plugging the values into both equations?
5. What are the possible outcomes when solving systems of equations (one solution, no solution, infinite solutions)?

**Tip:** Always simplify equations or expressions as much as possible before solving; it reduces the chance of errors!

solve each system by elimination
4x - 3y = -2
4x + 5y = 14

Learn how to solve the system of equations 4x - 3y = -2 and 4x + 5y = 14 using the elimination method. This detailed step-by-step guide explains how to eliminate one variable to find the solution (x = 1, y = 2). Ideal for students in Grades 8-10.

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