Simultaneous Equations - Quiz 1   Last unanswered question  Question  Next unanswered question

Question 1 lion

Solve the system simultaneous equations below
x + y = 4 (1)
x - y = 6. (2)
Which of the following is the value of x?
a) x = 10.   b) x = -1.
c) x = 2.   d) x = 5.

 

Not correct. Choice (a) is false.
Try again. You need to add the equations together to eliminate y .
Not correct. Choice (b) is false.
Try again. You need to add the equations together to eliminate y .
Not correct. Choice (c) 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 = 10 and hence x = 5. This then gives y = -1 since y = 4 -x = 4 - 5 = -1 and we check (2) and see that 5 - (-1) = 6. So we have that x = 5.
Question 2 lion

Solve the system simultaneous equations below
x+ 5y = -13
(1)
2x- y = 7.
(2)
Which of the following is the value of y?
a)       11
y = - 5-.    b) y = - 2.
c) y = - 7 .
     3    d) y = - 3.

 

Not correct. Choice (a) is false.
Try again. You need to multiply equation (1) by 2 and subtract the equations to eliminate x .
Not correct. Choice (b) is false.
Try again. You need to multiply equation (1) by 2 and subtract the equations to eliminate x .
Not correct. Choice (c) is false.
Try again. You need to multiply equation (1) by 2 and subtract the equations to eliminate x.
Your answer is correct.
Multiply equation (1) by 2 to give
2x+ 10y = -26
(3)
and subtract equation (2) from (3) we get
11y = -33 ==> y = -3.
Substituting y = - 3  into (1) we get x - 15 = - 13,  so x = 2.
Check in (2) and 2(2)-(-3)=4+3=7 and we have x = 2  and y = -3.
Question 3 lion

Consider the simultaneous equations below
5x + 2y = 9 (1)
9x - 7y = -5. (2)
Which of the following are the correct steps to eliminate x from the equations?
a) Multiply equation (1) by 7 and (2) by 2 and add the equations.
b) Multiply equation (1) by 9 and (2) by 5 and subtract the equations.
c) Multiply equation (1) by 7 and (2) by 2 and subtract the equations.
d) Multiply equation (1) by 9 and (2) by 5 and add the equations.

 

Not correct. Choice (a) is false.
Try again, this eliminates y .
Your answer is correct.
This then gives us
45x + 18y = 81
45x - 35y = -25.
When we subtract one from the other we get 53y = 106 and y = 2.
Not correct. Choice (c) is false.
Try again, you seem to be trying to eliminate y .
Not correct. Choice (d) is false.
Try again, this would not eliminate x but give us 90x - 17y = 56.
Question 4 lion

Solve the system of simultaneous equations below
5m - 6n = 12 (1)
2m + 9n = 20. (2)
Which of the following is the value of n?
a) n = 4
3.   b) n = -2.
c) n = 2.   d) n = -7.

 

Your answer is correct.
Solving by elimination we multiply (1) by 2 and (2) by 5.
10m - 12n = 24 (3)
10m + 45n = 100 (4)
Subtract equations (4) from (3) and get 57n = 76 so
n = 76
57 = 19 4
19-3- = 4
3.
Substitute n = 4
3 into equation (1) and get 5m- 6(4
3) = 12 so 5m = 12 + 8 = 20, so m = 4.
Check in equation (2), and 2(4) + 9(4
3) = 8 + 12 = 20 and we have m = 4 and n = 4
3.
Not correct. Choice (b) is false.
Try again. To solve by elimination we multiply (1) by 2 and (2) by 5.
Not correct. Choice (c) is false.
Try again. To solve by elimination we multiply (1) by 2 and (2) by 5.
Not correct. Choice (d) is false.
Try again. To solve by elimination we multiply (1) by 2 and (2) by 5.
Question 5 lion

Solve the system of simultaneous equations below
3w- 2z
-------
  2 = 9 (1)
6w- z
------
  5 = 9. (2)
Which of the following is the value of w ?
a) w = 1.   b) w = 10.
c) w = 8.   d) w = 3.

 

Not correct. Choice (a) is false.
Try again. To solve by elimination we multiply (1) by 2 and (2) by 5 to eliminate the fractions.
Not correct. Choice (b) is false.
Try again. To solve by elimination we multiply (1) by 2 and (2) by 5 to eliminate the fractions.
Your answer is correct.
Solving by elimination we multiply (1) by 2 and (2) by 5 to eliminate the fractions.
3w - 2z = 18 (3)
6w - z = 45 (4)
Multiply (4) by 2 to give
12w- 2z = 90
(5)
Subtract equation (3) from (5) and get 9w = 72, so w = 8. Substitute w = 8 into equation (4) and get 48 - z = 45 so z = 3.
Check in equation (3) and 3(8) - 2(3) = 24 - 6 = 18 and we have w = 8 and z = 3.
Not correct. Choice (d) is false.
Try again. To solve by elimination we multiply (1) by 2 and (2) by 5 to eliminate the fractions.