Arrange the steps to solve this system of linear equations in the correct sequence x+y=-2 2x-3y=-9

x+y=−2,              (i)2x−3y=−9.           (ii)

Multiplying equation (i) by 3, we have

\begin{gathered}3(x+y)=3\times(-2)Rightarrow 3x+3y=-6.(iii)\end{gathered}3(x+y)=3×(−2)⇒3x+3y=−6.               (iii)

Adding equations (ii) and (iii), we get

\begin{gathered}5x=-15Rightarrow x=-3.\end{gathered}5x=−15⇒x=−3.

Substituting the value of 'x' in equation (i), we get

\begin{gathered}-3+y=-2Rightarrow y=1.\end{gathered}−3+y=−2⇒y=1.

Thus, the solution set is (-3, 1).

Therefore, the correct steps in ascending order to solve the above system of equations are given below:

Step 1: (J) Multiply the first equation by 3: 3(x + y) = 3(-2) ⇒ 3x + 3y = -6.

Step 2: (F) Add 3x + 3y = -6 (obtained in step 1) to 2x – 3y = -9 (given), and solve for x.

Step 3: (G) x = -3.

Step 4: (B) Substitute the value of x in the first equation (x + y = -2) to get y = 1.  

Step 5:  (C) The solution for the system of equations is (-3, 1).

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step-by-step explanation: