Question

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

2 y2y
equals=
3 x plus 4
4 x minus 2 y
equals=
minus−4

Answer 1

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.