Simultaneous Equations - Quiz 3   Last unanswered question  Question  Next unanswered question

Question 1 lion

Solve the following system of simultaneous equations
x+ 5y = 34
(1)
x - 5y = - 6 .
(2)
Which of the following is the solution for  x ?
a) x = 4 .    b) x = - 1.
c) x = 14 .    d) x = 1.

 

Not correct. Choice (a) is false.
Try again, this is the value of y .
Not correct. Choice (b) is false.
Try again. You need to add the equations together to eliminate y.
Your answer is correct.
Solving by elimination we add the two equations and get  2x = 28    and hence  x = 14.
This then gives  y = 4    since by substitution into (1) we have       34--14-  20
y =   5    = 5 = 4    and we check (2) and see that  14 - 5(4) = - 6.  So we have that  x = 14    and  y = 4.
Not correct. Choice (d) is false.
Try again. You need to add the equations together to eliminate  y .
Question 2 lion

Solve the system of equations below.
2m + 3n = 14
(1)
4m  - 5n = 17.
(2)
Which of the following is the solution for  m .
a) m = 11.    b) m = 9.5.
c) m = 16.    d) m = - 9.5.

 

Not correct. Choice (a) is false.
Try again, this is the value of n.
Not correct. Choice (b) is false.
Try again, check the sign.
Not correct. Choice (c) is false.
Try again, multiply (1) by 2 to eliminate  m    and solve for  n    then find  m .
Your answer is correct.
Solving by elimination we multiply (1) by 2 to give
4n + 6n = 28
(3)
Subtract (2) from (3) to give  n = 11.    Substitute  n = 11    into (1) and
                               19
2m + 33 = 14 ⇒ 2m = - 19 ⇒ m = --2
Check in (2) and   - 38+ 55 = 17.    Hence  n = 11    and  m = 9.5.
Question 3 lion

Consider the simultaneous equations below
2x + 5y = 16
(1)
3x - 2y = 5.
(2)
Which of the following are the correct steps to eliminate x  from the equations?
a) Multiply (1) by 2 and (2) by 5 and then add the equations.
b) Multiply (1) by 3 and (2) by 2 and then add the equations.
c) Multiply (1) by 2 and (2) by -3 and then add the equations.
d) Multiply (1) by 3 and (2) by -2 and then add the equations.

 

Not correct. Choice (a) is false.
Try again, this eliminates y .
Not correct. Choice (b) is false.
Try again, you would need to subtract the equations to eliminate x .
Not correct. Choice (c) is false.
Try again, this gives   - 5x + 16y = 17.
Your answer is correct.
These steps give
6x+ 15y = 48
- 6x+ 4y = - 10.
and
19y = 38 ⇒ y = 2.
Question 4 lion

Which of the following is the solution for a to the simultaneous equations
2a +3b = - 5
(1)
3a - 2b = 12
(2)
a) a = 1 .    b) a = 5.
c) a = - 2.    d) a = 2 .

 

Not correct. Choice (a) is false.
Try again. To eliminate b  we multiply (1) by 2 and (2) by 3 and add the equations.
Not correct. Choice (b) is false.
Try again. To eliminate b  we multiply (1) by 2 and (2) by 3 and add the equations.
Not correct. Choice (c) is false.
Try again. To eliminate b  we multiply (1) by 2 and (2) by 3 and add the equations.
Your answer is correct.
Solving by elimination we multiply (1) by 2 and (2) by 3.
4a+ 6b = - 10
(3)
9a - 6b = 36
(4)
Add equations (3) and (4) and get   13a = 26    and hence  a = 2.
  Substitute  a = 2    into equation (1) and get   4+ 3b = - 5    so  b = - 3 .
Check in equation (2) and 3(2)-2(-3)=12 and we have   a = 2    and  b = - 3.
Question 5 lion

Consider the system of simultaneous equations below
5(2w - z) = 7w + 1
(1)
3(3w + z) = 5(w- z + 12) .
(2)
Which of the following is the correct simplification of the problem and solution for  w    to the system?
a)
3w- 5z = 1
w+ 2z = 15
and  w = 4.
b)
3w- 5z = 1
w + 2z = 4
and  w = 1.
c)
3w- 5z = 1
w+ 2z = 15
and  w = 7.
d)
3w- 5z = 1
w + 2z = 4
and  w = 2.

 

Not correct. Choice (a) is false.
Try again, you the correct equations but you have solved for z .
Not correct. Choice (b) is false.
Try again, you have not multiplied 12 by 5. These are the wrong equations but it is the correct solution for  z    to the wrong equations.
Your answer is correct.
Expanding the equations we have
10w - 5z = 7w + 1
9w+ 3z = 5w - 5z + 60
Collecting like terms we have
3w- 5z = 1
4w + 8z = 60
Dividing the last equation by 4 we have the required equations
3w- 5z = 1
(3)
w+ 2z = 15
(4)
Multiplying (4) by 3 we have
3w + 6z = 45
(5)
Subtract (3) from (5) and we have   11z = 44 ⇒ z = 4.    Substituting into (4) we have   w + 8 = 15 ⇒ w = 7
Check in (1) and we have  3(3 × 7+ 4) = 5(7- 4+ 12) = 75 .    Hence  w = 7.
Not correct. Choice (d) is false.
Try again, you have not multiplied 12 by 5. These are the wrong equations but it is the correct solution to the wrong equations.