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Simultaneous Equations
Quiz 1
Quiz 2
Quiz 3
Questions
right first
attempt
right
wrong
MathQuiz 4.2
University of Sydney
School of Mathematics
and Statistics
© Copyright 2004
Simultaneous Equations  Quiz 2
Question
Question 1
Which of the following is the solution for
in the simultaneous equations
(1)
(2)
a)
b)
c)
d)
Not correct. Choice
(a)
is
false
.
Try again, you need to add equations (
1
) and (
2
) to eliminate
Your answer is correct.
Solving by elimination we add the two equations and get
and hence
This then gives
since
and we check in (
2
)
and see that
So we have that
and
Not correct. Choice
(c)
is
false
.
Try again, you need to add equations (
1
) and (
2
) to eliminate
Not correct. Choice
(d)
is
false
.
Try again, you need to add equations (
1
) and (
2
) to eliminate
Question 2
Solve the system of simultaneous equations below.
(1)
(2)
Which of the following is the solution for
a)
b)
c)
d)
Not correct. Choice
(a)
is
false
.
Try again, you need to multiply equation (
1
) by 5 and subtract (
2
) from it.
Your answer is correct.
Multiply equation (
1
) by 5 to give
(3)
Subtract equation (
2
) from (
3
) to give
which
Substitute
into (
1
) and
which gives
Check in (
2
) and we have
Hence
and
Not correct. Choice
(c)
is
false
.
Try again, you need to multiply equation (
1
) by 5 and subtract (
2
) from it.
Not correct. Choice
(d)
is
false
.
Try again, you need to multiply equation (
1
) by 5 and subtract (
2
) from it.
Question 3
Consider the simultaneous equations below
(1)
(2)
Which of the following are the correct steps to eliminate
x
from the equations?
a)
Multiply equation (
1
) by 3 and (
2
) by 2 and subtract the equations.
b)
Multiply equation (
1
) by 3 and (
2
) by 2 and add the equations.
c)
Multiply equation (
1
) by 5 and (
2
) by 7 and subtract the equations.
d)
Multiply equation (
1
) by 5 and (
2
) by 7 and add the equations.
Your answer is correct.
This gives us
When we subtract one from the other we get
and
Not correct. Choice
(b)
is
false
.
Try again, this would not eliminate
but give us
Not correct. Choice
(c)
is
false
.
Try again, you have eliminated
Not correct. Choice
(d)
is
false
.
Try again, you seem to be trying to eliminate
Question 4
Consider the system of simultaneous equations below
(1)
(2)
Which of the following is the solution for
a)
b)
c)
d)
Your answer is correct.
Solving by elimination we multiply (
1
) by 3 and (
2
) by 2.
(3)
(4)
Subtract equations (
4
) from (
3
) and get
Substitute
into equation (
1
) and get
so
Check in equation (
2
)
and we have
and
Not correct. Choice
(b)
is
false
.
Try again, we multiply (
1
) by 3 and (
2
) by 2 to eliminate
Not correct. Choice
(c)
is
false
.
Try again, we multiply (
1
) by 3 and (
2
) by 2 to eliminate
Not correct. Choice
(d)
is
false
.
Try again, we multiply (
1
) by 3 and (
2
) by 2 to eliminate
Question 5
Consider the system of simultaneous equations below
(1)
(2)
Which of the following is the correct simplification of the problem and solution for
to the system?
a)
The system becomes
and
b)
The system becomes
and
c)
The system becomes
and
d)
The system becomes
and there is no solution to the system.
Not correct. Choice
(a)
is
false
.
The system is correct but the solution is incorrect.
Not correct. Choice
(b)
is
false
.
Try again, the system is incorrect but the value of
is correct for that system.
Your answer is correct.
and
(3)
(4)
When we multiply equation (
3
) by 3 and (
4
) by 11 we have
(5)
(6)
Adding equations (
5
) and (
6
) we have
Substituting into (
3
) we have
Check in (
3
) and we have
Hence
and
Not correct. Choice
(d)
is
false
.
Try again, you have not simplified the system correctly.