To determine which of the options will make the systems equivalent, we need to analyze the given equations.
You are provided with:
System A:
- \( 7x + 4y = -4 \)
System B:
2. \( 5x + 8y = 28 \)
To check for equivalence, we need to manipulate the first equation in some way to make it look like the second.
Option 1: \(-14x - 8y = -8\)
To see if this is equivalent, let's rewrite the first equation:
- Multiply \( 7x + 4y = -4 \) by \(-2\): \[ -2(7x + 4y) = -2(-4) \] This results in: \[ -14x - 8y = 8 \] This is not equal to \(-14x - 8y = -8\).
Option 2: \(-14x - 8y = 8\)
From our earlier operation, after multiplying the first equation by -2, we have: \(-14x - 8y = 8\), which we derived from the first equation. So, this makes the systems equivalent.
Option 3: \(-12x - 12y = 24\)
We will manipulate the first equation too:
- Multiply \( 7x + 4y = -4 \) by \(-\frac{12}{7}\) to compare: \[ -\frac{12}{7}(7x + 4y) = -\frac{12}{7}(-4) \] This doesn't transform it into the format of the other options. Thus, it is not equivalent.
Option 4: \(12x + 12y = 24\)
This does not match either equation, so it cannot represent an equivalent system.
Conclusion:
The correct option that makes the systems equivalent is:
−14x−8y=8.
1 answer