CHAPTER 5 KEY FORMULAS AND EQUATIONS

Linear equation in two unknowns

ax + by = c(5.1)

Definition of slope

m = y2 − y1x2 − x1(5.2)

Slope-intercept form

y = mx + b(5.3)

System of two linear equations

a1x + b1y = c1a2x + b2y = c2(5.4)

Second-order determinant

 | a1b1a2b2 |  = a1b2 − a2b1(5.8)

Cramer’s rule

x =  | c1b1c2b2 |  | a1b1a2b2 | andy =  | a1c1a2c2 |  | a1b1a2b2 | (5.9)

System of three linear equations

a1x + b1y + c1z = d1a2x + b2y + c2z = d2a3x + b3y + c3z = d3 (5.10)

Third-order determinant

 | a1b1c1a2b2c2a3b3c3 |  = a1b2c3 + a3b1c2 + a2b3c1 − a3b2c1 − a1b3c2 − a2b1c3 (5.12)

Cramer’s rule

x =  | d1b1c1d2b2c2d3b3c3 |  | a1b1c1a2b2c2a3b3c3 |  y =  | a1d1c1a2d2c2a3d3c3 |  | a1b1c1a2b2c2a3b3c3 |  z =  | a1b1d1a2b2d2a3b

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