Solve Using a Matrix by Elimination x-9=y , x+y=6

Problem

{[x−9=y],[x+y=6])

Solution

1. Rearrange the first equation into standard form a*x+b*y=c by subtracting y from both sides and adding 9 to both sides.

x−y=9

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

[[1,−1,|,9],[1,1,|,6]]

3. Eliminate the x term in the second row by replacing the second row ((R_2) with (R_2)−(R_1)

[[1,−1,|,9],[0,2,|,−3]]

4. Solve for y using the second row, which represents the equation 2*y=−3

y=−3/2

5. Substitute the value of y back into the first row's equation, x−y=9 to solve for x

x−(−3/2)=9

x+3/2=9

x=18/2−3/2

x=15/2

Final Answer

(x,y)=(15/2,−3/2)

Want more problems? Check here!