Simultaneous Equations - Quiz 2   Last unanswered question  Question  Next unanswered question

Question 1 lion

Which of the following is the solution for x  in the simultaneous equations
x + 7y = 5
(1)
x - 7y = - 9
(2)
a) x = -4.    b) x = -2 .
c) x = 2.    d) x = 3.

 

Not correct. Choice (a) is false.
Try again, you need to add equations (1) and (2) to eliminate y.
Your answer is correct.
Solving by elimination we add the two equations and get   2x = - 4    and hence  x = -2.
This then gives  y = 1    since      5- x   5 - (- 2)
y = --7--= ---7----= 1    and we check in (2)
and see that  -2- 7(1) = - 9.  So we have that x = -2  and y = 1 .
Not correct. Choice (c) is false.
Try again, you need to add equations (1) and (2) to eliminate y.
Not correct. Choice (d) is false.
Try again, you need to add equations (1) and (2) to eliminate y.
Question 2 lion

Solve the system of simultaneous equations below.
2a + 5b = 16
(1)
10a -3b = -4 .
(2)
Which of the following is the solution for b?
a) b = 2.    b) b = 3 .
c) b = 4.    d)     38
b = 11 .

 

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
10a+ 25b = 80 .
(3)
Subtract equation (2) from (3) to give   28b = 84    which  b = 3.
Substitute  b = 3    into (1) and  2a+ 15 = 16    which gives  a = 1.
    2
Check in (2) and we have     1
10(-) - 3(3) = 5 - 9 = - 4.
   2  Hence    1
a =-
   2    and  b = 3.
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 lion

Consider the simultaneous equations below
-2x + 7y = 4
(1)
-3x + 5y = - 5.
(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
- 6x + 21y = 12
-6x + 10y = - 10.
When we subtract one from the other we get  11y = 22    and   y = 2.
Not correct. Choice (b) is false.
Try again, this would not eliminate  x    but give us  - 12x + 31y = 2 .
Not correct. Choice (c) is false.
Try again, you have eliminated y.
Not correct. Choice (d) is false.
Try again, you seem to be trying to eliminate y.
Question 4 lion

Consider the system of simultaneous equations below
3x + 2y = 10
(1)
4x+ 3y = 13.
(2)
Which of the following is the solution for x?
a) x = 4.    b) x = 2.
c) x = 1.    d) x = -2.

 

Your answer is correct.
Solving by elimination we multiply (1) by 3 and (2) by 2.
9x + 6y = 30
(3)
8x + 6y = 26
(4)
Subtract equations (4) from (3) and get  x = 4.
Substitute  x = 4    into equation (1) and get  12 + 2y = 10  so  y = -1.
Check in equation (216 - 3 = 13    and we have   x = 4    and  y = -1 .
Not correct. Choice (b) is false.
Try again, we multiply (1) by 3 and (2) by 2 to eliminate y.
Not correct. Choice (c) is false.
Try again, we multiply (1) by 3 and (2) by 2 to eliminate y.
Not correct. Choice (d) is false.
Try again, we multiply (1) by 3 and (2) by 2 to eliminate y.
Question 5 lion

Consider the system of simultaneous equations below
3(m - n)- 8(m + n) = 7
(1)
2(m + n) +5(m - n) = -65.
(2)
Which of the following is the correct simplification of the problem and solution for  m    to the system?
a) The system becomes
5m + 11n = -7
7m - 3n = -65
and  m = 8.
b) The system becomes
5m + 11n = 7
7m - 3n = -65
and  m = 347 .
     46
c) The system becomes
5m + 11n = -7
7m - 3n = -65
and  m = - 8.
d) The system becomes
5m - 5n = - 7
7m - 7n = -65
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 m  is correct for that system.
Your answer is correct.
3(m - n) - 8(m + n) = 3m - 3n- 8m - 8n = -5m - 11n = 7
==> 5m + 11n = -7
and
2(m + n)+ 5(m - n) = 2m +2n + 5m - 5n = - 65
==> 7m - 3n = -65.
5m + 11n = -7
(3)
7m - 3n = -65
(4)
When we multiply equation (3) by 3 and (4) by 11 we have
15m + 33y = -21
(5)
77m - 33y = -715.
(6)
Adding equations (5) and (6) we have   92m  = -736 ==> m = - 8.
Substituting into (3) we have  -40+ 11n = -7 ==> 11n = 33 ==> n = 3 .
Check in (3) and we have   7(-8)- 3(3) = -56 - 9 = - 65.  Hence  m = - 8    and  n = 3.
Not correct. Choice (d) is false.
Try again, you have not simplified the system correctly.