Practice Questions
Concept Explanation
Simultaneous equations are two or more equations with the same variables, solved together for a unique (or consistent) solution set.
Methods
- Substitution: Express one variable in terms of the other and substitute.
- Elimination: Add or subtract equations (or multiply first) to eliminate one variable.
Example
x + y = 10 and x − y = 2. Add: 2x = 12, x = 6. Then y = 4.
Common Trap
Check the solution in both original equations. Arithmetic slips in elimination are common.
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Q1 Easy
If x + y = 10 and x − y = 2, what is the value of x?
ExplanationAdding: 2x = 12, so x = 6. -
Q2 Easy
If x + y = 10 and x − y = 2, what is the value of y?
Explanationx = 6, so y = 10 − 6 = 4. -
Q3 Easy
For the simultaneous equations 2x + y = 11 and x + y = 7, what is the value of x?
ExplanationSubtract: x = 4. -
Q4 Easy
For the simultaneous equations 2x + y = 11 and x + y = 7, what is the value of y?
Explanationx = 4, so y = 7 − 4 = 3. -
Q5 Medium
If x + 2y = 8 and 2x + y = 7, what is the value of x + y?
ExplanationFrom elimination: x = 2, y = 3. x + y = 5. -
Q6 Medium
For the system 3x + 2y = 16 and 2x + 3y = 14, what is the value of x?
ExplanationElimination gives x = 4, y = 2. -
Q7 Medium
For the system 3x + 2y = 16 and 2x + 3y = 14, what is the value of y?
ExplanationElimination gives x = 4, y = 2.
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Q8 Medium
If 2x + 3y = 13 and x + y = 5, what is the value of y?
ExplanationSubstitute x = 5 − y: 2(5 − y) + 3y = 13 gives y = 3. -
Q9 Hard
There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
Explanationx − 10 = y + 10 and x + 20 = 2(y − 20) give x = 100, y = 80. -
Q10 Hard
If x/3 + y/2 = 5 and x + y = 12, what is the value of x?
ExplanationMultiply first by 6: 2x + 3y = 30. With x + y = 12: x = 6, y = 6. -
Q11 Hard
If 3x + 4y = 20 and 2x + 3y = 14, what is the value of xy?
ExplanationSolution: x = 4, y = 2. xy = 8. -
Q12 Medium
For the system 5x + 2y = 19 and 3x + 2y = 13, what is the value of x?
ExplanationSubtract: 2x = 6, so x = 3. -
Q13 Easy
If x + y = 12 and 2x − y = 3, what is the value of 2x + 2y?
Explanation2x + 2y = 2(x + y) = 2 × 12 = 24. -
Q14 Hard
If x − y = 4 and x + y = 12, what is the value of x² − y²?
Explanationx² − y² = (x + y)(x − y) = 12 × 4 = 48.
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DS1 Easy
What are the values of x and y that satisfy the system x + y = 10 and x − y = 2?
Statement Ix + y = 10.
Statement IIx − y = 2.
ExplanationNeed both equations to determine x = 6 and y = 4 uniquely. -
DS2 Easy
What is the value of x in the system of equations 2x + y = 11 and x + y = 7?
Statement I2x + y = 11.
Statement IIx + y = 7.
ExplanationNeed both: subtract to get x = 4.
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DS3 Medium
What is the value of y in the system 3x + 2y = 16 and 2x + 3y = 14?
Statement I3x + 2y = 16.
Statement II2x + 3y = 14.
ExplanationTwo independent linear equations in two unknowns; need both. -
DS4 Medium
What is the value of x + y if x + 2y = 8 and 2x + y = 7?
Statement Ix + 2y = 8.
Statement II2x + y = 7.
ExplanationNeed both: x = 2, y = 3, so x + y = 5.