ABSTRACT
When solving linear simultaneous equations in two unknowns using determinants:
write the equations in the form a 1 x + b 1 y + c 1 = 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq2737.tif"/> a 2 x + b 2 y + c 2 = 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq2738.tif"/>
the solution is given by: x D x = − y D y = 1 D https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq2739.tif"/>
where D x = | b 1 c 1 b 2 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/eq2740.tif"/> i.e. the determinant of the coefficients left when the x-column is covered up,
D y = | a 1 c 1 a 2 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/eq2741.tif"/> i.e. the determinant of the coefficients left when the y-column is covered up,
and D = | 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/eq2742.tif"/> i.e. the determinant of the coefficients left when the constants-column is covered up
