Question

System A System B 7x+4y=−4 5x+8y=28 7x+4y=−4 ? Which of the following terms will make the systems equivalent? (1 point) Responses −14x−8y=−8 negative 14 x minus 8 equals negative 8 12x+12y=24 12 x plus 12 y equals 24 −12x−12y=24 negative 12 x minus 12 y equals 24 −14x−8y=8

Answer 1

In order to make the two systems equivalent, we need to find a term that, when applied, would produce the same solution set.

We know that if two equations are equivalent, one can be transformed into the other by multiplying the entire equation by a non-zero constant.

Let’s analyze the first equation in the system:

1. \(7x + 4y = -4\)

To find an equivalent equation, we can multiply both sides by the same constant. Let's explore the options given:

1. \(-14x - 8y = -8\)
- This can be derived by multiplying the entire original equation by -2:
\[
-2(7x + 4y) = -2(-4) \implies -14x - 8y = 8
\]
(This is not equivalent as the right-hand side does not match.)

2. \(12x + 12y = 24\)
- This does not produce an equivalent equation from the original equation.

3. \(-12x - 12y = 24\)
- This is also not derived from the original equation.

4. \(-14x - 8y = 8\)
- This can be derived just like the first option but results in the right-hand side being positive 8 after multiplication by -2.

After reviewing the equations, the valid transformation that leads to an equivalent system to \(7x + 4y = -4\) is:

**−14x−8y=8**

Thus, the correct option is:

**−14x−8y=8**.