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Solving two equations of 1 st degree

Solving two equations of 1 st degree. Find the S.S. of the following equations. X + Y = 5 , X – Y = 3. Solution. X + Y = 5 eq (1). +. X – Y = 3 eq (2). . X = 4. 2X = 8. Sub in eq (1).

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Solving two equations of 1 st degree

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  1. Solving two equations of 1st degree Find the S.S. of the following equations X + Y = 5 , X – Y = 3 Solution X + Y = 5 eq (1) + X – Y = 3 eq(2)  X = 4 2X = 8 Sub in eq (1) X + Y = 5  4 + Y = 5  Y = 1 S.S = { ( 4 , 1 ) }

  2. Find the S.S. of the following equations X – Y = 4 , 3X + 2Y = 7 Solution X – Y = 4 eq(1) ×2 3X + 2Y = 7 eq(2) ×1 2X – 2Y = 8 + 3X + 2Y = 7 5X = 15  X = 3 Sub in eq(2) 3X +2Y = 7  9 + 2Y = 7  Y = -1 S.S = { ( 3 , -1 ) }

  3. Find the S.S. of the following equations X + 3Y = 5 ,2X + 6Y = 10 Solution X + 3Y = 5 eq(1) ×-6 2X + 6Y = 10 eq(2) ×3 -6X – 18Y = -30 + 6X + 18Y = 30 Infinite numbers of S.S 0 = 0 S.S = { ( x , y ) : X + 3Y = 5 } OR S.S = { ( x , y ) : 2X + 6Y =10 }

  4. Find the S.S. of the following equations 3X + Y = 4 ,2Y + 6X = 3 Solution 3X + Y = 4 eq(1) ×-2 6x + 2y = 3 eq(2) ×1 -6X – 2Y = -8 + 6X + 2Y = 3 Has no solution 0 = -5 S.S = { } or Ø

  5. Remarks • If the two equations a1 X + b1 Y = c1 and a2 X + b2 Y = c2 have • One solution • if ≠ ≠ represented graphically by 2 intersected lines • Infinite number of solutions • if = = represented graphically by 2 coincide lines • No solution • if = ≠ represented graphically by 2 parallel lines

  6. Complete • The S.S. of the two lines X = 1 , Y = 3 is …………… • 2) The S.S. of the two lines X – 3 = 0 , Y + 4 = 0 is ………. • 3) If the two lines X + 3Y = 4 and X + aY = 7 are parallel then a = ……… • 4) If the two lines X + 4Y = 7 , 3X + kY = 21 have infinite number of • solutions then k = …… Answer 1) { (1 , 3) } 2) { (3 , -4) } 3) 3 4) 12 H.W Page 8 third no 1 ( b , e , f )

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