Simultaneous Equations

Question 1

Which of the following is the solution for $x$ in the simultaneous equations

x + 7y = 5

(1)

x - 7y = - 9

(2)

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

Solve the system of simultaneous equations below.

2a + 5b = 16

(1)

10a -3b = -4 .

(2)

Which of the following is the solution for $b?$

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

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?

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

Consider the system of simultaneous equations below

3x + 2y = 10

(1)

4x+ 3y = 13.

(2)

Which of the following is the solution for $x?$

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 (2) $16 - 3 = 13$ 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

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?

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.


		Faculty of Economics and Business MathQuiz