Question 1
LEVEL 4
Solve the following simultaneous equations:
7x+3y=6
5x+5y=6
Select the correct answer from the list below:
A: x = 0.6, y = 0.6
B:x = 0.4, y = 0.8
C:x = 0.6, y = 0.3
D:x = 1.2, y = 0.4
CORRECT ANSWER: A: x = 0.6, y = 0.6
WORKED SOLUTION:
First we have to multiply the top equation by 5 and the bottom equation by 3 so the coefficients match,
35x+15y=30
15x+15y=18
So now we have a way to remove one of the variables by subtracting one of the equations from the other,
20x=12
x=\dfrac{12}{20}=\dfrac{6}{10}=0.6
Substituting this value back into one of the original equations we find
5(0.6)+5y=6
3+5y=6
5y=3
y=0.6
ANSWER: x = 0.6, y = 0.6
Question 2
LEVEL 4
Solve the following simultaneous equations:
y=x+1
y=4x-2
Select the correct answer from the list below:
A: x = 2, y = 2
B: x = 1, y = 2
C: x =2, y = 1
D:x = 1, y = 1
CORRECT ANSWER: C: x = 1, y = 2
WORKED SOLUTION:
First we can find x by setting the two equations equal to one another,
x+1=4x-2
3x=3
x=1
Substituting this value back into one of the original equations we find
y=x+1
y=2
ANSWER: x = 1, y = 2
Question 3
LEVEL 4
2 rooms and 5 spa treatments cost \pounds 1005
6 rooms and 2 spa treatments cost \pounds 1728.
All spa treatments and rooms cost the same, calculate the cost of a room.
Select the correct answer from the list below:
A: £99
B: £255
C: £1287
D: £6630
CORRECT ANSWER: B: £255
WORKED SOLUTION:
Attach variables to the information in the question:
Let the price of a room =r, and
Let the price of spa a treatment =s.
Then
2r + 5s = 1005
6r + 2s = 1728
Multiply the top equation by 3 so that the coefficients are the same:
6r + 15s = 3015
6r + 2s = 1728
Remove the r variable by subtracting the second equation from the first to find the other, we get
13s = 1287
So
s = 99
Substituting back into the original equations, we find
2r + 5(99) = 1005
2r = 510
r = 255
So
Room = \pounds 255
Spa = \pounds 99
Answer = \pounds 255 per room
Question 4
LEVEL 4
Solve the following simultaneous equations:
y=\frac{3}{14} x+\frac{5}{7}
y=2x-10
Select the correct answer from the list below:
A: x = 6, y = 2
B: x = 3, y = 8
C: x = -2, y = 6
D: x = 6, y = 4
CORRECT ANSWER: A: x = 6, y = 2
WORKED SOLUTION:
First we can find x by setting the two equations equal to one another,
\frac{3}{14} x+\frac{5}{7}=2x-10
3x+10=28x-140
150=25x
x=6
Substituting this value back into one of the original equations we find
y=2x-10
y=2
ANSWER: x = 6, y = 2
Question 5
LEVEL 4
Solve the following simultaneous equations:
y=-\frac{5}{2} x+10
y=-x+8.5
Select the correct answer from the list below:
A: x = 4, y = 3.5
B: x = 1, y = 7.5
C: x = -1, y = 8.5
D: x = 1, y = 4.5
CORRECT ANSWER: B: x = 1, y = 7.5
WORKED SOLUTION:
First we can find x by setting the two equations equal to one another,
-x+8.5=-2.5 x+10
1.5x=1.5
x=1
Substituting this value back into one of the original equations we find
y=-x+8.5
y=7.5
ANSWER: x = 1, y = 7.5