logging in or signing up Determinants joshsmith1110 Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 654 Category: Education License: All Rights Reserved Like it (1) Dislike it (0) Added: March 13, 2009 This Presentation is Public Favorites: 1 Presentation Description No description available. Comments Posting comment... Premium member Presentation Transcript 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 You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.
Determinants joshsmith1110 Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 654 Category: Education License: All Rights Reserved Like it (1) Dislike it (0) Added: March 13, 2009 This Presentation is Public Favorites: 1 Presentation Description No description available. Comments Posting comment... Premium member Presentation Transcript 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