2-Variable Equations & Inequalities Online Practice

Question

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13 of 1813 of 18 Items

Question
Use the table to answer the question.

System A System B
5x+2y=−3


3x+3y=9


3x+3y=9


?


Which of the following terms will make the systems equivalent?

(1 point)
Responses

−8x−5y=6
negative 8 x minus 5 y equals 6

−10x+4y=6
negative 10 x plus 4 y equals 6

8x+5y=6
8 x plus 5 y equals 6

−10x−4y=−6
negative 10 x minus 4 y equals negative 6
Remaining Attempts : 3
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Answer 1

To determine which equation from the options will make System B equivalent to System A, we need to manipulate the equations in System A and check against the options provided.

First, let's rewrite the equation in System A:

1. System A: \[ 5x + 2y = -3 \] \[ 3x + 3y = 9 \]

Next, we can express the second equation in System B in a simpler form:

• Divide the entire second equation of System B by 3: \[ x + y = 3 \] This does not change its equivalency, as dividing an equation by a non-zero number does not affect its solutions.

Now, let's analyze what would make the two systems equivalent. The equations must result in the same solution set.

Now check the options provided:

1. Option 1: \( -8x - 5y = 6 \)
2. Option 2: \( -10x + 4y = 6 \)
3. Option 3: \( 8x + 5y = 6 \)
4. Option 4: \( -10x - 4y = -6 \)

We notice that System B has \( 3x + 3y = 9 \) as its second equation. Thus, we expect to find transformations of \( 3x + 3y = 9 \) that will relate to any of the options given.

Let's analyze them.

We need to find equivalent forms for \( 5x + 2y = -3 \).

1. Checking \( -10x + 4y = 6 \):

Rearranging:

• Multiply the first equation by 2 (to match the coefficients of y).
• The system is still not matching.

2. Checking \( 8x + 5y = 6 \):

Assuming \( 5x + 2y = -3 \) or \( 3x + 3y = 9 \)

3. Checking \( -10x - 4y = -6 \):

This doesn't match with the first system.

And finally,

4. Checking \( -8x - 5y = 6 \):

We find suitable equivalents, e.g., Rearranging:

Thus, the most likely option that provides an equivalent form should be equivalent to the expected return \( 5x + 2y = -3 \).

Based on typical outcomes and simplifications, you would select the equation from what proven equivalently gives the same outcome.

Choose the One Likely Matched:

Analyzing the transformations, you find it correctly matches original roots wherein,

Potentially: It looks like Option 1 is more likely.

Therefore, the right response to find the combination giving equivalency seems more aligned to option −10x+4y=6. Adjusting this into transformed states fits back into the equation sequence.