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13.4 Simultaneous equations 2

13.4 Simultaneous equations 2

Look again at these simultaneous equations from the last topic.
x + y = 83
x − y = 18
Another way to solve them is to add the equations together.
(x + y) + (x − y) = 83 + 18
The two y terms cancel.
A 2x = 101
A x = 50.5
Substitute this value in the 'rst equation: 50.5 + y = 83 A y = 83 − 50.5 = 32.5

!is method works because the coe(cients of y (1 and –1) The coeffi cient is the number

add up to 0. multiplying the unknown.
Worked example 13.4

Solve the simultaneous equations: 5x + y = 27
2x + y = 6

Subtract the second equation from the fi rst.
(5x + y) − (2x + y) = 27 − 6 Subtraction cancels out the y terms.
3x = 21 Collect like terms.
A x = 7
Substitute in the second equation.
2 × 7 + y = 6 You could also substitute into the fi rst equation.
A y = 6 − 14 = −8

) Exercise 13.4

1 Solve each of these pairs of simultaneous equations. Use any method you like.
a x + y = 15 b x + y = 30 c x + y = 2
x − y = 3 x − y = 1 x − y = 14
2 Here are two simultaneous equations. 2x + y = 19
3x − y = 21

a Add the two sides of these equations and use the result to find the value of x.
b Find the value of y.
3 Here are two simultaneous equations. x + 6y = 9
x + 2y = 1
a Subtract the two sides of the equations and use the result to find the value of y.

b Find the value of x.
4 Here are two simultaneous equations. 3x + 2y = 38 Will you add or subtract
x − 2y = 2 to eliminate y?
a Find the value of 4x.
b Find the values of x and y.
5 Solve these simultaneous equations. Use any method you wish.
a 2x + y = 22 b y = 2x − 12 c 2x + y = 0
x − y = 5 x + y = 3 x + 2y = 12
13 Equations and inequalities 129