KS4 Grade 9 - SIMULTANEOUS EQUATIONS
Lesson 2...SIMULTANEOUS LINEAR AND NON-LINEAR EQUATIONS IN TWO UNKNOWNS
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A pair of simultaneous equations, one linear and the other non-linear, can generally be solved using the substitution method.
Firstly, obtain an equation in one unknown by substitution (as in Lesson 1) and solve it for this unknown.
Next, use the linear equation to fins the other unknown.
TASK - Textbook Pg34 Ex 2.2
HOMEWORK - None set
Firstly, obtain an equation in one unknown by substitution (as in Lesson 1) and solve it for this unknown.
Next, use the linear equation to fins the other unknown.
TASK - Textbook Pg34 Ex 2.2
HOMEWORK - None set
Lesson 1...SIMULTANEOUS LINEAR EQUATIONS IN TWO UNKNOWNS
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SIMULTANEOUS EQUATIONS are two, or more, equations which contain two, or more, unknowns and must be solved in conjunction with one another to calculate the values of the unknowns.
Simultaneous linear equations may be solved either by substitution or by elimination. Both methods are demonstrated below.
Eg. 2x + 3y = 7..........(1)
3x - 4y = 2...........(2)
SUBSTITUTION -
From (1):
x = (7 - 3y)/2..........(3)
Substituting (3) into (2) gives
3[(7 - 3y)/2] - 4y = 2..........(4)
(4) x 2 gives
3(7 - 3y) - 8y = 4 --> 21 - 9y - 8y = 4 --> 21 - 17y = 4 --> 17 = 17y --> y = 1
Substituting y = 1 into (3) gives x = 2
ELIMINATION -
To eliminate y:
(1) x 4 gives 8x + 12y = 28.........(3)
(2) x 3 gives 9x - 12y = 6...........(4)
(3) + (4): 17x = 34
x = 2
Substitute x = 2 into (1) gives y = 1
TASK 1 - Textbook Pg31 Ex2.1
Simultaneous linear equations may be solved either by substitution or by elimination. Both methods are demonstrated below.
Eg. 2x + 3y = 7..........(1)
3x - 4y = 2...........(2)
SUBSTITUTION -
From (1):
x = (7 - 3y)/2..........(3)
Substituting (3) into (2) gives
3[(7 - 3y)/2] - 4y = 2..........(4)
(4) x 2 gives
3(7 - 3y) - 8y = 4 --> 21 - 9y - 8y = 4 --> 21 - 17y = 4 --> 17 = 17y --> y = 1
Substituting y = 1 into (3) gives x = 2
ELIMINATION -
To eliminate y:
(1) x 4 gives 8x + 12y = 28.........(3)
(2) x 3 gives 9x - 12y = 6...........(4)
(3) + (4): 17x = 34
x = 2
Substitute x = 2 into (1) gives y = 1
TASK 1 - Textbook Pg31 Ex2.1