Determinants

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INTRODUCTION : 

INTRODUCTION A system of two linear equations in variables x and y has the form a1x + b1y = c1 a2x + b2y = c2

Slide 2: 

The values for x and y can be solve into five solutions/processes. This includes 1. Elimination 2. Substitution 3. Comparison 4. Graphing 5. Determinants a1 = ? b1 = ? c1 = ? a2 = ? b2 = ? c2 = ?

Slide 3: 

Solving a system of two linear equations in variables x and y using the determinants.

DEFINITION OF A DETERMINANTS : 

DEFINITION OF A DETERMINANTS Determinants is a 2 x 2 matrix. EXAMPLE A = a1 b1 a2 b2 ( ) B = c1 b1 c2 b2 ( ) C = a1 c1 a2 c2 ( ) X = ) 7 3 -5 (

FORMULA : 

FORMULA For x : c1 b1 c2 b2 a1 b1 a2 b2 numerator denominator For y : a1 c1 a2 c a1 b1 a2 b2 = a1 c2 a1 b2 – a2 c1 – a2 b1 = a1 b2 – a2 b1 c2 b1 c1 b2 –

EXAMPLE : 

EXAMPLE (1.) 2x+3y = 4 (2.) x + 2y = -7 X = ? Y = ? a1 = 2 b1 = 3 c1 = 4 ; ; a2 = 1 ; b2 = 2 ; c2 = -7

Slide 7: 

GIVEN: a1 = 2 ; b1 = 3 ; c1 = 4 a2 = 1 ; b2 = 2 ; c2 = -7 SOLUTION : For x c1 b1 c2 b2 a1 b1 a2 b2 = 3 -7 2 3 1 2 = 8 – (-21) 4 - 3 = 29 1 = 29

GIVEN: a1 = 2 ; b1 = 3 ; c1 = 4 a2 = 1 ; b2 = 2 ; c2 = -7 : 

GIVEN: a1 = 2 ; b1 = 3 ; c1 = 4 a2 = 1 ; b2 = 2 ; c2 = -7 For y a1 c1 a2 c2 a1 b1 a2 b2 = 4 1 -7 3 1 2 = -14 - 4 4 - 3 = -18 1 = -18

Checking : 1st equation : 

Checking : 1st equation X = 29 Y = -18 2x + 3y = 4 2(29) + 3(-18) = 4 58 – 54 = 4 4 = 4

Checking : 2nd equation : 

Checking : 2nd equation X = 29 Y = -18 29 + 2(-18) = -7 -7 = -7 X + 2y = -7 29 + (-36) = -7

Slide 11: 

THE END

Presented By; Shella P. Paglinawan : 

Presented By; Shella P. Paglinawan BSEd Math-4