Solve Using a Matrix by Elimination 9c-3d=-33 , 6c+5d=-8

Problem

{[9*c−3*d=−33],[6*c+5*d=−8])

Solution

1. Write the system of linear equations as an augmented matrix.

[[9,−3,|,−33],[6,5,|,−8]]

2. Simplify the first row by dividing all elements by 3 to make the numbers easier to work with.

1/3*(R_1)→(R_1)

[[3,−1,|,−11],[6,5,|,−8]]

3. Eliminate the c term in the second row by subtracting twice the first row from the second row.

(R_2)−2*(R_1)→(R_2)

[[3,−1,|,−11],[0,7,|,14]]

4. Solve for d by dividing the second row by 7

1/7*(R_2)→(R_2)

[[3,−1,|,−11],[0,1,|,2]]

d=2

5. Eliminate the d term in the first row by adding the second row to the first row.

(R_1)+(R_2)→(R_1)

[[3,0,|,−9],[0,1,|,2]]

6. Solve for c by dividing the first row by 3

1/3*(R_1)→(R_1)

[[1,0,|,−3],[0,1,|,2]]

c=−3

Final Answer

(c,d)=(−3,2)

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