ABSTRACT
The procedure for solving linear simultaneous equations in two unknowns using matrices is:
write the equations in the form a 1 x + b 1 y = c 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq2693.tif"/> a 2 x + b 2 y = c 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq2694.tif"/>
write the matrix equation corresponding to these equations, i.e. ( a 1 b 1 a 2 b 2 ) × ( x y ) = ( c 1 c 2 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq2695.tif"/>
determine the inverse matrix of ( a 1 b 1 a 2 b 2 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq2696.tif"/> i.e. 1 a 1 b 2 − b 1 a 2 ( b 2 − b 1 − a 2 a 1 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq2697.tif"/>
multiply each side of (ii) by the inverse matrix, and
solve for x and y by equating corresponding elements
