5.4 Solving Systems of Two Linear Equations in Two Unknowns by Determinants

  • Determinant of the Second Order • Cramer’s Rule • Solving Systems of Equations by Determinants

Consider two linear equations in two unknowns, as given in Eqs. (5.4):

a1x + b1y = c1a2x + b2y = c2(5.4)

If we multiply the first of these equations by b2 and the second by b1 ,  we obtain

a1b2x + b1b2y = c1b2a2b1x + b2b1y = c2b1(5.5)

We see that the coefficients of y are the same. Thus, subtracting the second equation from the first, we can solve for x. The solution can be shown to be

x = c1b2 − c2b1a1b2 − a2b1(5.6)

In the same manner, we may show that

y = a1c2 − a2c1a1b2 − a2b1(5.7)

The expression a1b2 − a2b1 ,  which appears in each of the denominators of Eqs. (5.6)

Get Basic Technical Mathematics, 11th Edition now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.