# Question 3.3: Given the simultaneous equations 2x + 3y = 0.75 (1) 5x + 2y ......

Given the simultaneous equations

2x + 3y = 0.75                   (1)
5x + 2y = 6                        (2)

Solve for x and y algebraically.

Step-by-Step
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In these two equations, neither the x- nor the y-terms are the same. If equation (1) is multiplied by 2 and equation (2) is multiplied by –3, the y-terms in both equations will be the same with opposite signs. Then proceed as in Worked Example 3.1 above.

Step 1: Eliminate y-terms from the system of equations:

4x + 6y = 1.5             (1)× 2

$\underline {−15x − 6y = 18}$    (2)×−3

x = $\frac {−16.5}{−11}$= 1.5        solving for x

Step 2: Solve for y by substituting x = 1.5 into either equation (1) or equation (2):

2(1.5) + 3y = 0.75        substituting x = 1.5 into equation (1)

3y = 0.75 − 3

y = $\frac {−2.25}{3}$

Step 3: Checking the solution: x = 1.5,    y = $−\frac {2.25}{3}$ is left as an exercise for the reader.

Question: 3.21

## A firm receives £2.5 per unit for a particular good. The fixed costs incurred are £44 while each unit produced costs £1.4. (a) Write down the equations for (i) total revenue, and (ii) total cost. (b) Calculate the break-even point algebraically. (c) If the government imposes a tax of £0.70 per unit ...

(a)     (i) TR = P × Q = 2.5Q (ii) TC = FC + VC = ...
Question: 3.22

## (a) Show graphically that the equilibrium price and quantity for the demand and supply functions given by the pairs of equations (i) and (ii) is the same.(i) Pd = 120 − 2Q Ps = 10 + 2Q and (ii) Pd = 120 − 2Q Ps = 37.5 + Q (b) If a tax of 20 is imposed on each unit produced, recalculate the ...

(a) The table of points and the graphs of equation...
Question: 3.16

## In a two-sector economy, autonomous consumption expenditure, C0 = £50m, autonomous investment expenditure, I0 = £100m, and b = 0.5. (a) Determine (i) the equilibrium level of national income, Ye, and (ii) the equilibrium level of consumption, Ce, algebraically. (b) Plot the consumption function, ...

(a) (i) Step 1: Households’ consumption expenditur...
Question: 3.12

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Question: 3.6

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The simplest approach is to add equation (3) to eq...
Question: 3.2

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(a) In this example, neither the x- nor the y-term...
Question: 3.15

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(a) The algebraic solution to this part is given o...
Question: 3.14

## The total revenue and total cost functions are given as follows: TR = 3Q (3.23) TC = 10 + 2Q (3.24) (a) Calculate the equilibrium quantity algebraically and graphically at the break-even point. (b) Calculate the value of total revenue and total cost at the break-even point. ...

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Question: 3.13