Question

Consider the followimg three systems of linear equations.System A{2x - 5y = 11 [A1]{7x - 8y = 10 [A2]System B{2x - 5y = 11 [B1]{x + 7y = -23 [B2]System C{-19y = 57 [C1){x + 7y = -23 [C2]Answer the questions below. (shown in picture)For each, choose the transformation and the fill in the blank with the correct number. The arrow meand the expression on the left becomes the expression on the right.

Answer 1

We have the following:

1.

$\begin{gathered} \text{ System A} \\ 2x-5y=11\lbrack A1\rbrack \\ 7x-8y=10\lbrack A2\rbrack \\ \text{ System B} \\ 2x-5y=11\lbrack B1\rbrack \\ x+7y=-23\lbrack B2\rbrack \\ \text{Transform System A into System B} \\ A1=B1 \\ -3\cdot A1+A2\rightarrow B2 \\ -3\cdot2x--3\cdot5y=-3\cdot11 \\ -6x+15y=-33 \\ 7x-8y=10\lbrack \\ x+7x=-23 \end{gathered}$

The answer is the third option

2.

$\begin{gathered} \text{ System B} \\ 2x-5y=11\lbrack B1\rbrack \\ x+7y=-23\lbrack B2\rbrack \\ \text{ System C} \\ -19y=57\lbrack C1\rbrack \\ x+7y=-23\lbrack C2\rbrack \\ \text{Transform System B into System C} \\ B2=C2 \\ -2\cdot B2+B1\rightarrow C1 \\ -2\cdot x+-2\cdot7y=-2\cdot-23 \\ -2x-14y=46 \\ 2x-5y=11 \\ 0x-19y=57 \\ -19y=57 \end{gathered}$

Therefore the answer is the last option