Question

System A System B
−x+y=1

x+y=11

x+y=11

?

Which of the following shows the equation that creates a true equivalent system?

(1 point)
Responses

−2x−2y=−22
negative 2 x minus 2 y equals negative 22

2x+2y=12
2 x plus 2 y equals 12

−x−y=−1
negative x minus y equals negative 1

2y=12

Answer 1

To find an equation that creates a true equivalent system with the given equations from System A and System B, we first need to examine the equations closely.

From System A:
1. \(-x + y = 1\)

From System B:
1. \(x + y = 11\)

Now let's solve the equation from System A for \(y\):
\[
y = x + 1
\]

Next, we substitute \(y\) into the equation from System B:
\[
x + (x + 1) = 11
\]
\[
2x + 1 = 11
\]
\[
2x = 10
\]
\[
x = 5
\]

Using the value of \(x\), we can find \(y\):
\[
y = 5 + 1 = 6
\]

Thus, the solution of the system is \(x = 5\) and \(y = 6\).

Now, let's check the proposed equations for equivalence:

1. **\(-2x - 2y = -22\)**: This equation can be simplified by dividing through by -2, resulting in \(x + y = 11\), which is equivalent to an equation in System B.

2. **\(2x + 2y = 12\)**: Dividing this by 2 gives \(x + y = 6\), which is not equivalent to the original systems.

3. **\(-x - y = -1\)**: This rearranges to \(x + y = 1\), which is again not equivalent to the original systems.

4. **\(2y = 12\)**: This simplifies to \(y = 6\). This does not account for the value of \(x\) and does not show an equivalent relationship.

The only equation that creates a true equivalent system is:
**\(-2x - 2y = -22**.

So the correct response is:

**−2x−2y=−22** (negative 2 x minus 2 y equals negative 22).