Linear Simultaneous Equations Flashcards
What do you do when you have 2 symbols that are the same?
minus the equations
What do you always have to do after you have found both x and y?
check using the other equation
Solve: 3a + 2b = 17
4a - b = 30
4a - b = 30
4a = 30 + b
b = 4a - 30
3a + 2(4a - 30) = 17 3a - 60 + 8a = 17 11a - 60 = 17 11a = 77 a = 7
(7 x 3) + 2b = 17
21 + 2b = 17
2b = -4
b = -2
4a - b = 30
(4 x 7) - (-2) = 30
28 + 2 = 30
Solve: 4x + 3y = 27
5x - 2y = 5
4x + 3y = 27 (x2)
5x - 2y = 5 (x3)
8x + 6y = 54
15x - 6y = 15
23x = 69
x = 3
4x + 3y = 27
12 + 3y = 27
3y = 15
y = 5
5x - 2y = 5
15 - 10 = 5
What do you do when you have 2 different symbols?
add the equations
Other than adding/subtracting the equations, how else can you solve them?
by finding x or y and substituting it in
Solve: 6x + y = 15
4x + y = 11
6x + y = 15 -
4x + y = 11
= 2x + 0 = 4
x = 4/2
x = 2
(4 x 2) + y = 11
8 + y = 11
y = 11 - 8 y = 3
6x + y = 15
12 + 3 = 15
OR
6x + y = 15
y = 15 - 6x
4x + (15 - 6x) = 11
-2x + 15 = 11
-2x = -4
x = 2
(4 x 2) + y = 11
8 + y = 11
y = 3
6x + y = 15
12 + 3 =15
Mr and Mrs Smith take their two children to the cinema. The total cost is £33. Mr Jones takes his three children to the cinema and the total cost is £27.50. Calculate the price of a child ticket and an adult ticket.
2c + 2a = 33
3c + a = 27.50
a = 27.5 - 3c
2c + 2(27.5 - 3c) = 33 2c + 55 - 6c = 33 -4c + 55 = 33 -4c = -22 c = 5.5
(2 x 5.5) + 2a = 33
11 + 2a = 33
2a = 22
a = 11
3c + a = 27.5
(3 x 5.5) + 11 = 27.5
16.5 + 11 = 27.5
A child ticket is £5.50, and an adult ticket is £11.
Solve: 3x + 2y = 18
2x - y = 5
2x - y = 5
2x = 5 + y
y = 2x - 5
3x + 2(2x - 5) = 18 3x + 4x - 10 = 18 7x - 10 = 18 7x = 28 x = 4
12 + 2y = 18
2y = 6
y = 3
2x - y = 5
8 - 3 = 5
OR
3x + 2y = 18
2x - y = 5 (x2)
3x + 2y = 18
4x - 2y = 10
7x = 28 x = 4
12 + 2y = 18
2y = 6
y = 3
2x - y = 5
8 - 3 = 5
What do you do if you are solving by adding/subtracting and none of the coefficients are equal?
multiply one or both of the equations to make them equal
Person A rents out a building for 10 days. The total cost is £155. Person B rents out a building for 7 days. The total cost is £123.5. There is a set fee and a cost per day, what are they?
10d + x = 155
7d + x = 123.5
x = 155 - 10d 7d + 155 - 10d = 123.5 -3d + 155 = 123.5 -3d = -31.5 d = 10.5
(7 x 10.5) + x = 123.5
73.5 + x = 123.5
x = 50
10d + x = 155
105 + 50 = 155
£50 is the set fee and £10.50 is the cost per day.
Give a step by step process of how to solve 2 linear simultaneous equations.
0) multiply one or both equations if necessary
1) minus/add them together
2) solve to find x or y
3) substitute the value into an equation
4) solve
5) check using the other equation
OR
1) rearrange to equal x or y
2) substitute the value into the other equation
3) solve
4) substitute the new value into an equation to find x or y
5) check using the other equation
How do you solve from a graph?
Find the point where the 2 lines cross
