Faithannr123idn
Answered

Expand your horizons with the diverse and informative answers found on IDNLearn.com. Get prompt and accurate answers to your questions from our experts who are always ready to help.

System A
[tex]\[
\begin{array}{l}
-x-2y = 7 \\
5x-6y = -3 \\
\text{Solution: } (-3, -2)
\end{array}
\][/tex]

Choose the correct option that explains what steps were followed to obtain the system of equations below.

System B
[tex]\[
\begin{aligned}
-x - 2y &= 7 \\
-16y &= 32
\end{aligned}
\][/tex]

A. To get System B, the second equation in System A was replaced by the sum of that equation and the first equation multiplied by 5. The solution to System B will be the same as the solution to System A.

B. To get System B, the second equation in System A was replaced by the sum of that equation and the first equation multiplied by -5. The solution to System B will not be the same as the solution to System A.

C. To get System B, the second equation in System A was replaced by the sum of that equation and the first equation multiplied by -6. The solution to System B will not be the same as the solution to System A.

D. To get System B, the second equation in System A was replaced by the sum of that equation and the first equation multiplied by 3. The solution to System B will be the same as the solution to System A.

Sagot :

GinnyAnsweridn
Let's analyze the transformations to go from System A to System B step-by-step.

System A:
[tex]\[ \begin{array}{l} -x - 2y = 7 \quad \text{(Equation 1)}\\ 5x - 6y = -3 \quad \text{(Equation 2)} \end{array} \][/tex]

System B:
[tex]\[ \begin{array}{l} -x - 2y = 7 \quad \text{(Equation 1)}\\ -16y = 32 \quad \text{(Equation 2')} \end{array} \][/tex]

We are given four options to identify how Equation 2 in System A was transformed to Equation 2' in System B:

### Testing Option A:
> A. The second equation in system A was replaced by the sum of that equation and the first equation multiplied by 5.

1. Multiply the first equation by 5:
[tex]\[ 5(-x - 2y) = 5 \times 7 \implies -5x - 10y = 35 \][/tex]

2. Add this result to the second equation in System A:
[tex]\[ (5x - 6y) + (-5x - 10y) = -3 + 35 \][/tex]
[tex]\[ -16y = 32 \][/tex]

This matches Equation 2' in System B. Thus, option A describes the correct transformation.

### Verifying other options:

#### Option B:
> B. The second equation in system A was replaced by the sum of that equation and the first equation multiplied by -5.

1. Multiply the first equation by -5:
[tex]\[ -5(-x - 2y) = -5 \times 7 \implies 5x + 10y = -35 \][/tex]

2. Add this result to the second equation in System A:
[tex]\[ (5x - 6y) + (5x + 10y) = -3 - 35 \][/tex]
[tex]\[ 10x + 4y = -38 \][/tex]

This does not match Equation 2' in System B.

#### Option C:
> C. The second equation in system A was replaced by the sum of that equation and the first equation multiplied by -6.

1. Multiply the first equation by -6:
[tex]\[ -6(-x - 2y) = -6 \times 7 \implies 6x + 12y = -42 \][/tex]

2. Add this result to the second equation in System A:
[tex]\[ (5x - 6y) + (6x + 12y) = -3 - 42 \][/tex]
[tex]\[ 11x + 6y = -45 \][/tex]

This does not match Equation 2' in System B.

#### Option D:
> D. The second equation in system A was replaced by the sum of that equation and the first equation multiplied by 3.

1. Multiply the first equation by 3:
[tex]\[ 3(-x - 2y) = 3 \times 7 \implies -3x - 6y = 21 \][/tex]

2. Add this result to the second equation in System A:
[tex]\[ (5x - 6y) + (-3x - 6y) = -3 + 21 \][/tex]
[tex]\[ 2x - 12y = 18 \][/tex]

This does not match Equation 2' in System B.

### Conclusion:
The correct option is:
A. To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by 5. The solution to system B will be the same as the solution to system A.
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com provides the best answers to your questions. Thank you for visiting, and come back soon for more helpful information.