Solve the system by either the elimination method or the substitution method.

To solve the system of equations given, we first need to clearly define them. From your text, it seems there might be a typo or confusion in the formatting. I will interpret the system as follows:

1. \( 2y = 3x + 4 \)
2. \( 4x - 2y = -4 \)

Step 1: Solve the first equation for \(y\)

From the first equation, we can express \(y\) in terms of \(x\): \[ 2y = 3x + 4 \] \[ y = \frac{3x + 4}{2} \]

Step 2: Substitute \(y\) into the second equation

Now we substitute \(y\) in the second equation: \[ 4x - 2y = -4 \] Replacing \(y\) gives: \[ 4x - 2\left(\frac{3x + 4}{2}\right) = -4 \]

Step 3: Simplify the equation

The equation simplifies as follows: \[ 4x - (3x + 4) = -4 \] \[ 4x - 3x - 4 = -4 \] \[ x - 4 = -4 \]

Step 4: Solve for \(x\)

Now, we solve for \(x\): \[ x = 0 \]

Step 5: Substitute back to find \(y\)

Substituting \(x = 0\) back into the equation for \(y\): \[ y = \frac{3(0) + 4}{2} = \frac{4}{2} = 2 \]

Step 6: Conclusion

Thus, the solution to the system of equations is: \[ x = 0, \quad y = 2 \]

This can be represented as the ordered pair \((0, 2)\).

Verification

To verify, we can substitute \((0, 2)\) back into the original equations:

1. For \(2y = 3x + 4\): \[ 2(2) = 3(0) + 4 \quad \Rightarrow \quad 4 = 4 \quad \text{(True)} \]

2. For \(4x - 2y = -4\): \[ 4(0) - 2(2) = -4 \quad \Rightarrow \quad -4 = -4 \quad \text{(True)} \]

Both equations are satisfied, confirming that the solution \((0, 2)\) is correct.