Problem

Solve the following system of equations using matrix elimination method: 3x−2y=7 and 5x+y=11

Answer

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Answer

Finally, we can see that x = 3315 and y = -213

Steps

Step 1 ：First, we write this system of equations in matrix form: [3−2 51][x y]=[7 11]

Step 2 ：Next, we perform row operations to transform the coefficient matrix into row-echelon form. Multiply the first row by 5 and the second row by 3: [15−10 153][x y]=[35 33]

Step 3 ：Subtract the second row from the first row: [0−13 153][x y]=[2 33]

Step 4 ：Divide the first row by -13 and the second row by 15 to get the identity matrix: [01 10][x y]=[−213 3315]

Step 5 ：Finally, we can see that x = 3315 and y = -213

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