Question```latex Three systems of linear equations.
$\begin{array}{c} \text{System B} \\ \left\{ \begin{array}{c} -5x + 2y = 4 \quad [\mathrm{B}1] \\ -13x = 26 \quad [\mathrm{B}2] \end{array} \right. \end{array} \quad \begin{array}{c} \text{System C} \\ \left\{ \begin{array}{c} -5x + 2y = 4 \quad [\mathrm{C}1] \\ x = -2 \quad [\mathrm{C}2] \end{array} \right. \end{array}$
Below, transformation and then fill in the
How do we transform System B into System C?
$\times$ Equation $[B 1] \rightarrow$ Equation [C1]
Equation $[B 2] \rightarrow$ Equation [C2]
Equation $[B 1]+$ Equation $[B 2] \rightarrow$ Equation $[C 2]$
Equation $[B 2]+$ Equation $[B 1] \rightarrow$ Equation [C1]

Studdy Solution

STEP 1

1. We have two systems of linear equations, System B and System C.
2. We need to transform System B into System C using the given operations.

STEP 2

1. Analyze the equations in System B.
2. Analyze the equations in System C.
3. Determine the transformation steps needed to convert System B into System C.

STEP 3

Analyze System B: - Equation $[B1]$ : $-5x + 2y = 4$ - Equation $[B2]$ : $-13x = 26$

STEP 4

Analyze System C: - Equation $[C1]$ : $-5x + 2y = 4$ - Equation $[C2]$ : $x = -2$

STEP 5

Determine the transformation from System B to System C: - Equation $[C1]$ is identical to Equation $[B1]$ , so no transformation is needed for this equation. - To transform Equation $[B2]$ into Equation $[C2]$ , solve $-13x = 26$ for $x$ : $ -13x = 26 \implies x = \frac{26}{-13} = -2 \] This matches Equation \([C2]\).
The transformation from System B to System C involves recognizing that Equation $[B1]$ is already in the form of Equation $[C1]$ and solving Equation $[B2]$ to find $x = -2$ , which is Equation $[C2]$ .
The correct transformation is: - Equation $[B1]$ becomes Equation $[C1]$ . - Solving Equation $[B2]$ gives Equation $[C2]$ .

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