Solving Simultaneous Equations Using Elimination Quick Check

Question

1 of 51 of 5 Items
Question
Use the table to answer the 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

2y=12
2 y equals 12

−x−y=−1
negative x minus y equals negative 1
Skip to navigation

Answer 1

To find the equation that creates a true equivalent system to the given systems, we can manipulate one of the original equations. Here we have:

For System A: \[ -x + y = 1 \]

For System B (which has the same equation): \[ x + y = 11 \]

An equivalent system can be derived by multiplying the entire equation by a constant.

1. Let's multiply the first equation \(-x + y = 1\) by -2 to create an equivalent equation:

\[ -2(-x + y) = -2(1) \] This simplifies to: \[ 2x - 2y = -2 \]

2. Rearranging gives: \[ 2x - 2y + 2 = 0 \] This is equivalent to: \[ 2x - 2y = -2 \]

This is similar to the option provided; however, we need to further analyze the given options:

• −2x−2y=−22: This is not equivalent since it is not consistent with the multiplier used.
• 2x+2y=12: Not equivalent.
• 2y=12: Not equivalent.
• −x−y=−1: This is just a rearrangement of the original equation \(-x + y = 1\).

None of these options give us the exact manipulation needed.

However, if we focus and summarize which option might relate closely to the transformations: The equation -x - y = -1 is indeed equivalent to the first equation multiplied by -1.

Thus, the most suitable choice would be:

−x−y=−1