Method of substitution MCQs With Answer

Introduction: The Method of Substitution is a fundamental algebraic technique used to solve systems of linear equations commonly encountered in pharmaceutical calculations. For B. Pharm students, mastering substitution simplifies solving concentration, dilution, and mixture problems in pharmaceutics, pharmacokinetics and compounding. This SEO-friendly guide emphasizes practical steps, application examples, and exam-ready MCQs to strengthen analytical skills for lab work and exam preparation. Learn how to isolate variables, substitute accurately, check solutions, and apply the method to real-world drug formulation and dose calculations. Building fluency in substitution boosts speed and accuracy in competitive exams and professional tasks. Now let’s test your knowledge with 50 MCQs on this topic.

Q1. What is the first step in the method of substitution when solving two linear equations?

• Add both equations together
• Isolate one variable in one equation
• Graph both equations
• Multiply both equations by constants

Correct Answer: Isolate one variable in one equation

Q2. If you have equations x + y = 10 and x – y = 2, what is x using substitution?

• 4
• 6
• 8
• 2

Correct Answer: 6

Q3. In a mixture problem, 2 L of 5% solution is mixed with x L of 12% solution to make 10 L of 9% solution. Which equation represents the total volume?

• 2 + x = 10
• 0.05(2) + 0.12(x) = 0.09(10)
• x – 2 = 10
• 2x = 10

Correct Answer: 2 + x = 10

Q4. After isolating x = 8 – y from x + y = 8, what is the next substitution step?

• Substitute x = 8 – y into the other equation
• Differentiate the equation
• Solve for y using a graph
• Square both sides

Correct Answer: Substitute x = 8 – y into the other equation

Q5. When is substitution preferred over elimination?

• When coefficients are the same
• When one variable is already isolated or easily isolated
• When solving nonlinear equations only
• When there are more than three variables

Correct Answer: When one variable is already isolated or easily isolated

Q6. Solve by substitution: 3x + 2y = 12 and x = 2y. What is y?

• 2
• 1
• 3
• 4

Correct Answer: 2

Q7. In pharmaceutical dilution, if C1V1 + C2V2 = CfinalVfinal, how can substitution help?

• It eliminates the need for concentration units
• It allows solving for an unknown volume or concentration by replacing one variable with an expression from another equation
• It converts percentages to molarity automatically
• It avoids balancing equations

Correct Answer: It allows solving for an unknown volume or concentration by replacing one variable with an expression from another equation

Q8. For equations 2x – y = 5 and x + 3y = 11, substitute x = (5 + y)/2 into second equation. What is y?

• 1
• 2
• 3
• 4

Correct Answer: 2

Q9. What common mistake should be checked after solving by substitution?

• Ignoring unit conversions
• Not verifying solutions in the original equations
• Using negative numbers
• Graphing results

Correct Answer: Not verifying solutions in the original equations

Q10. In compounding, a pharmacist mixes A mg and B mg to achieve a target ratio. Which method helps convert the ratio into simultaneous equations?

• Method of substitution
• Boiling point elevation
• Titration
• Chromatography

Correct Answer: Method of substitution

Q11. Solve: x + 2y = 14 and x = 4y – 2. What is x?

• 6
• 10
• 8
• 12

Correct Answer: 10

Q12. When substituting, what must you maintain to avoid algebra errors?

• Ignore parenthesis
• Maintain sign and grouping symbols correctly
• Change coefficients arbitrarily
• Round intermediate values early

Correct Answer: Maintain sign and grouping symbols correctly

Q13. For equations 5x + y = 26 and y = 2x + 1, substitute y into first. What is x?

• 3
• 4
• 2
• 5

Correct Answer: 5

Q14. A drug formulation needs 3% and 8% solutions to obtain 5% final concentration. Using substitution, which variable is convenient to isolate?

• Total mass
• Volume of one of the solutions
• pH
• Temperature

Correct Answer: Volume of one of the solutions

Q15. If x = 3y and 4x + y = 25, substitution yields which quadratic or linear result for y?

• Linear: 13y = 25
• Linear: 12y + y = 25
• Quadratic: 4(3y)^2 + y = 25
• No solution

Correct Answer: Linear: 13y = 25

Q16. Solve using substitution: 6x – 3y = 9 and y = 2x – 1. What is x?

• 1
• 2
• 3
• 4

Correct Answer: 1

Q17. In pharmacokinetics, when two equations relate dose and concentration, substitution helps to:

• Estimate bioavailability without algebra
• Eliminate a variable to predict concentration from dose
• Measure blood pressure
• Calculate pKa directly

Correct Answer: Eliminate a variable to predict concentration from dose

Q18. System: x/2 + y = 9 and x = 4. Using substitution, what is y?

• 7
• 5
• 3
• 1

Correct Answer: 5

Q19. How does substitution handle nonlinear terms like x^2 when found in the second equation?

• Never applicable
• Substitute the expression and solve resulting nonlinear equation by algebraic methods
• Change to elimination only
• Approximate with decimals

Correct Answer: Substitute the expression and solve resulting nonlinear equation by algebraic methods

Q20. If two strengths of active ingredient yield a final strength, which equation form is typical before substitution?

• C1V1 + C2V2 = CfinalVfinal
• pH = pKa + log
• F = (AUC oral)/(AUC IV)
• Rate = k[C]

Correct Answer: C1V1 + C2V2 = CfinalVfinal

Q21. Solve: x – 3y = 4 and 2x + y = 1 by substitution. What is x?

• 1
• 2
• 3
• 4

Correct Answer: 1

Q22. In substitution, when isolating a fractional variable, which is important?

• Clear denominators by multiplication before substituting
• Ignore the fraction
• Round the fraction immediately
• Convert to percentage

Correct Answer: Clear denominators by multiplication before substituting

Q23. A compounding problem: 10 mL of 2% ointment mixed with x mL of 10% ointment to yield 6% in (10 + x) mL. Which equation gives active amount?

• 0.02(10) + 0.10(x) = 0.06(10 + x)
• 10 + x = 6
• 0.02 + 0.10 = 0.06
• x = 10

Correct Answer: 0.02(10) + 0.10(x) = 0.06(10 + x)

Q24. After substituting and solving, you get a negative volume. What does this indicate?

• Correct physical solution
• Error in setup, wrong equations or sign mistake
• Acceptable for concentrations
• Need to double units

Correct Answer: Error in setup, wrong equations or sign mistake

Q25. Solve: 7x + 2y = 20 and x = 2 – y. What is y?

• 1
• 2
• 3
• 0

Correct Answer: 1

Q26. Which step verifies the correctness of substitution results?

• Plugging the solved values into original equations
• Discarding the solution
• Changing variable names
• Using elimination instead

Correct Answer: Plugging the solved values into original equations

Q27. For 4x – y = 7 and y = 3x – 2, substitution yields what x?

• 1
• 2
• 3
• 4

Correct Answer: 1

Q28. In mixing two medications for desired potency, why is substitution helpful?

• It predicts patient response
• It calculates required volumes or masses to achieve target potency by solving simultaneous equations
• It sterilizes the mixture
• It measures viscosity

Correct Answer: It calculates required volumes or masses to achieve target potency by solving simultaneous equations

Q29. Solve: x/3 + y/2 = 5 and x = 6 – y. What is y?

• 2
• 3
• 4
• 5

Correct Answer: 3

Q30. When substituting into an equation with decimals, best practice is to:

• Convert decimals to fractions if it simplifies algebra
• Always round early
• Drop decimals
• Use only calculators without algebra

Correct Answer: Convert decimals to fractions if it simplifies algebra

Q31. Solve by substitution: 9x – y = 17 and y = x + 1. What is x?

• 2
• 3
• 4
• 1

Correct Answer: 2

Q32. In pharmacology, two linear relations between clearance and dose are given. Substitution helps you to:

• Find the intersection point representing a specific regimen
• Measure drug pKa
• Calculate melting point
• Impute missing pharmacokinetic samples

Correct Answer: Find the intersection point representing a specific regimen

Q33. Solve: 2(x + y) = 16 and x = 3y. What is y?

• 2
• 3
• 4
• 1

Correct Answer: 2

Q34. If substitution leads to a quadratic equation, how many real solutions might you get?

• Zero, one, or two depending on discriminant
• Always one
• Always two complex
• Always infinite

Correct Answer: Zero, one, or two depending on discriminant

Q35. A tablet contains 50 mg active and 150 mg filler. If x tablets give a total of 2000 mg active, and each pack has y tablets, which method converts pack equations to solve for x and y?

• Method of substitution
• Thin layer chromatography
• Mass spectrometry
• pH titration

Correct Answer: Method of substitution

Q36. Solve: x + y = 20 and y = 2x – 5. What is x?

• 5
• 8
• 10
• 7

Correct Answer: 5

Q37. Which is a benefit of substitution when teaching B. Pharm students?

• It clarifies variable relationships in formulation problems
• It removes the need for lab skills
• It replaces dose calculations
• It increases experimental error

Correct Answer: It clarifies variable relationships in formulation problems

Q38. Solve: 5(x – 1) + y = 14 and x = 2y. What is y?

• 1
• 2
• 3
• 4

Correct Answer: 2

Q39. In practice problems, substitution can be combined with unit conversion. What should you do first?

• Substitute then convert units
• Convert units first, then substitute into consistent equations
• Ignore units during substitution
• Use elimination instead

Correct Answer: Convert units first, then substitute into consistent equations

Q40. Solve: 3x + 4y = 24 and x = y + 2. What is x?

• 4
• 5
• 6
• 3

Correct Answer: 4

Q41. A pharmacist must achieve 0.5% concentration from 1% and 0.1% stocks. Which unknown is easiest to isolate for substitution?

• Amount of 0.1% stock
• Amount of 0.5% final
• Temperature
• pH

Correct Answer: Amount of 0.1% stock

Q42. Solve: x – y = 8 and y = (x – 2)/3. What is x?

• 11
• 12
• 10
• 9

Correct Answer: 12

Q43. If substitution yields complex roots for concentrations, what does this imply?

• Physically acceptable concentrations
• Error in model or setup; concentrations must be real
• Concentrations are negative
• Solution is valid for pH only

Correct Answer: Error in model or setup; concentrations must be real

Q44. For simultaneous equations derived from mass balance and potency, substitution helps to:

• Ignore mass balance
• Find the unknown mass or potency by eliminating one variable
• Change chemical properties
• Strengthen bonding

Correct Answer: Find the unknown mass or potency by eliminating one variable

Q45. Solve: 8x + y = 50 and y = 2x + 10. What is x?

• 4
• 5
• 6
• 3

Correct Answer: 4

Q46. In substitution, when dealing with three variables and three equations, what is a practical approach?

• Isolate one variable and substitute into remaining two equations, reducing to two-variable system
• Use substitution only on two equations and guess the third
• Never use substitution for three variables
• Randomly assign values

Correct Answer: Isolate one variable and substitute into remaining two equations, reducing to two-variable system

Q47. Solve: x + 4 = 2y and 3x – y = 5 by substitution. What is y?

• 3
• 2
• 1
• 4

Correct Answer: 3

Q48. Why is careful algebra important when substituting expressions containing parentheses?

• Parentheses can be dropped safely
• Incorrect distribution leads to wrong coefficients and solutions
• Parentheses only affect aesthetics
• They convert linear to quadratic always

Correct Answer: Incorrect distribution leads to wrong coefficients and solutions

Q49. Solve: 2x + 3y = 22 and x = 5 – y. What is x?

• 3
• 4
• 5
• 2

Correct Answer: 3

Q50. For exam preparation, which practice best improves proficiency with substitution?

• Practicing diverse problems including mixture, dilution, and kinetics and checking solutions step-by-step
• Only memorizing formulas without practice
• Skipping verification steps
• Using calculators without understanding

Correct Answer: Practicing diverse problems including mixture, dilution, and kinetics and checking solutions step-by-step

G S Sachin

I am a Registered Pharmacist under the Pharmacy Act, 1948, and the founder of PharmacyFreak.com. I hold a Bachelor of Pharmacy degree from Rungta College of Pharmaceutical Science and Research. With a strong academic foundation and practical knowledge, I am committed to providing accurate, easy-to-understand content to support pharmacy students and professionals. My aim is to make complex pharmaceutical concepts accessible and useful for real-world application.

Mail- Sachin@pharmacyfreak.com