Solve Using a Matrix by Elimination 5x+3=4y , y=8x-2

Problem

{[5*x+3=4*y],[y=8*x−2])

Solution

1. Rearrange the equations into standard form a*x+b*y=c to prepare for the augmented matrix.

5*x−4*y=−3

−8*x+y=−2

2. Write the augmented matrix representing the system of linear equations.

[[5,−4,|,−3],[−8,1,|,−2]]

3. Eliminate the y term in the first row by adding 4 times the second row to the first row ((R_1)←(R_1)+4*(R_2).

5+4*(−8)=−27

−4+4*(1)=0

−3+4*(−2)=−11

[[−27,0,|,−11],[−8,1,|,−2]]

4. Solve for x by dividing the first row by −27 ((R_1)←(R_1)/(−27).

[[1,0,|,11/27],[−8,1,|,−2]]

5. Eliminate the x term in the second row by adding 8 times the first row to the second row ((R_2)←(R_2)+8*(R_1).

−8+8*(1)=0

1+8*(0)=1

−2+8*(11/27)=−54/27+88/27=34/27

[[1,0,|,11/27],[0,1,|,34/27]]

Final Answer

(x,y)=(11/27,34/27)

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