Simultaneous Equations : Simultaneous Equations OCR Module 8
What are they? : What are they? Simply 2 equations
With 2 unknowns
Usually x and y
To SOLVE the equations means we find values of x and y that
Satisfy BOTH equations [work in]
At same time [simultaneously]
Elimination Method : Elimination Method 2x – y = 1 3x + y = 9 We have the same number of y’s in each If we ADD the equations, the y’s disappear + 5x = 10 Divide both sides by 5 x = 2 A B Substitute x = 2 in equation A 2 x 2 – y = 1 4 – y = 1 y = 3 Answer
x = 2, y = 3
Slide 4 : Elimination Method 5x + y = 17 3x + y = 11 We have the same number of y’s in each If we SUBTRACT the equations,
the y’s disappear - 2x = 6 Divide both sides by 2 x = 3 A B Substitute x = 3 in equation A 5 x 3 + y = 17 15 + y = 17 y = 2 Answer
x = 3, y = 2
Slide 5 : Elimination Method 2x + 3y = 9 2x + y = 7 We have the same number of x’s in each If we SUBTRACT the equations,
the x’s disappear - 2y = 2 Divide both sides by 2 y = 1 A B Substitute y = 1 in equation A 2x + 3 = 9 2x = 6 x = 3 Answer
x = 3, y = 1
Slide 6 : Elimination Method 4x - 3y = 14 2x + 3y = 16 We have the same number of y’s in each If we ADD the equations,
the y’s disappear + 6x = 30 Divide both sides by 6 x = 5 A B Substitute x = 5 in equation A 20 – 3y = 14 3y = 6 y = 2 Answer
x = 5, y = 2
Basic steps : Basic steps Look at equations
Same number of x’s or y’s?
If the sign is different, ADD the equations otherwise subtract tem
Then have ONE equation
Solve this
Substitute answer to get the other
CHECK by substitution of BOTH answers
What if NOT same number of x’s or y’s? : What if NOT same number of x’s or y’s? 5x + 2y = 17 3x + y = 10 - x = 3 In B A B 5 x 3 + 2y = 17 15 + 2y = 17 y = 1 Answer
x = 3, y = 1 If we multiply A by 2 we
get 2y in each 5x + 2y = 17 6x + 2y = 20 B A
Slide 9 : What if NOT same number of x’s or y’s? 3x + 6y = 21 4x - 2y = 8 + 15x = 45 In B A B 3 x 3 + 6y = 21 6y = 12 y = 2 Answer
x = 3, y = 2 If we multiply A by 3 we
get 6y in each 3x + 6y = 21 12x - 6y = 24 B A x = 3
Slide 10 : …if multiplying 1 equation doesn’t help? 3x + 7y = 26 5x + 2y = 24 - 29y = 58 In B A B 5x + 2 x 2 = 24 5x = 20 x = 4 Answer
x = 4, y = 2 Multiply A by 5 & B by 3,
we get 15x in each 15x + 35y = 130 15x + 6y = 72 B A y = 2 Could multiply A by 2 & B
by 7 to get 14y in each
Slide 11 : …if multiplying 1 equation doesn’t help? 3x - 2y = 7 5x + 3y = 37 + 19x = 95 In B A B 5 x 5 + 3y = 37 3y = 12 y = 4 Answer
x = 5, y = 4 Multiply A by 3 & B by 2,
we get +6y & -6y 9x – 6y = 21 10x + 6y = 74 B A x = 5 Could multiply A by 5 & B
by 3 to get 15x in each