Solve Using an Augmented Matrix -8x-3y=-8 , -6x-y=-4

Problem

{[−8*x−3*y=−8],[−6*x−y=−4])

Solution

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

[[−8,−3,|,−8],[−6,−1,|,−4]]

2. Divide the first row (R_1) by −8 to create a leading 1 in the first column.

[[1,3/8,|,1],[−6,−1,|,−4]]

3. Eliminate the xterm in the second row by replacing (R_2) with (R_2)+6*(R_1)

[[1,3/8,|,1],[0,5/4,|,2]]

4. Multiply the second row (R_2) by 4/5 to create a leading 1 in the second column.

[[1,3/8,|,1],[0,1,|,8/5]]

5. Eliminate the yterm in the first row by replacing (R_1) with (R_1)−3/8*(R_2)

[[1,0,|,2/5],[0,1,|,8/5]]

6. Identify the values of x and y from the resulting reduced row echelon form.

x=2/5

y=8/5

Final Answer

(x,y)=(2/5,8/5)

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