Simultaneous Equations - Word Questions
Equations that must be solved at the same time are simultaneous equations.
E.g.1
The sum of two numbers is 6 and the difference is 2. Find the numbers.
Let the numbers be x and y.
x + y = 6 ---
1
x - y = 2 ---
2
1 +
2 => 2x = 8
x = 4
Sub in
1=> 4 + y = 6
y = 2
The numbers are x = 4 and y = 2.
E.g.2
The sum of two books and a pencil is £6.00. The difference of cost between 3 books and 2 pencils is £2.00. Find the cost of a book and a pencil.
Let the cost of a book be x and that of a pencil be y.
2x + y = 6 ---
1
3x - 2y = 2 ------
1
1 X 2 => 4x + 2y = 12 ------
3
2 +
1 => 7x = 14
x = 2
Sub in
1
4 + y = 6
y = 2
The cost of a book and a pencil is £2.00 each.
E.g.3
If I double a number and add three times a second number, the answer is 1. If I multiply the first number by 3 and take away twice the second number, the answer is 8. Find the numbers.
Let the numbers be x and y.
2x + 3y = 1 ---
1
3x - 2y = 8 ---
2
From
1 - 3y => 2x = (1 - 3y)
x = (1 - 3y)/2
Sub in
2 => 3(1 - 3y)/2 - 2y = 8
X 2 => 3(1 - 3y) - 4y = 16
3 - 9y - 4y = 16
3 - 13y = 16
-3 => -13y = 13
y = -1
Sub in
1 => 2x - 3 = 1
+ 3 => 2x = 4
x = 2
The numbers are x = 2 and y = -1.
E.g.4
The sum of twice the cost of a box biscuits and the cost of a box chocolates is £8.00. The difference between the cost of box of chocolates and the box of biscuits is £1.00. Find the cost of each.
Let the cost of the box chocolates and the box of biscuits be y and x respectively.
2x + y = 8 ---
1
y -x = 1 ---
2
1 => y = 8 - 2x
Sub in
2 => y = 8 - 2x - x = 1
8 - 3x = 1
-8 => -3x = -9
:- -3 => x = 3
Sub in
1 => 6 + y = 8
-6 => y = 2
The cost of box of chocolates =£2.00 and that of biscuits = £3.00.
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