System A System B

Question

−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).