Solving Simultaneous equation using matrix Method Question: Find the values of x and y in the equations below 3 x + 2 y = 6 5 x − y = 8 Using matrix method Put the equations in standard form and then use matrices to solve the system of equations. 3 x + 2 y = 6 , 5 x − y = 8 Write the equations in matrix form ( 3 5 2 − 1 ) ( x y ) = ( 6 8 ) Left multiply the equation by the inverse matrix of ( 3 5 2 − 1 ) . i n v e r s e ( ( 3 5 2 − 1 ) ) ( 3 5 2 − 1 ) ( x y ) = i n v e r s e ( ( 3 5 2 − 1 ) ) ( 6 8 ) The product of a matrix and its inverse is the identity matrix ( 1 0 0 1 ) ( x y ) = i n v e r s e ( ( 3 5 2 − 1 ) ) ( 6 8 ) Multiply the matrices on the left hand side of the equal sign. ( x y ) = i n v e r s e ( ( 3 5 2 − 1 ) ) ( 6 8 ) For the 2 × 2 matrix ( a c b d ) , the inverse matrix is ( a d − b c d a d − b c − c a d − b c − b a d − b c a ) , so the matrix equation can be ...
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