Linear Equation in Two Variables Quiz: Test Your Knowledge
Challenge your skills in solving linear equations in two variables with this interactive quiz. Test your ability to find solutions for various systems of equations.
Linear Equation in Two Variable Questions and Answers
- 1.
What is the solution for 2x + 3y = 12 and x - y = 2?
- A.
X = 2, y = 2
- B.
X = 3, y = 1
- C.
X = 1, y = 3
- D.
X = 4, y = 0
Correct Answer
A. X = 2, y = 2Explanation
To solve the system 2x + 3y = 12 and x - y = 2, first isolate x from the second equation: x = y + 2. Substitute x = y + 2 into the first equation: 2(y + 2) + 3y = 12. Simplifying, 2y + 4 + 3y = 12, which becomes 5y = 8. Therefore, y = 8/5. Substituting y = 8/5 back into x = y + 2 gives x = 8/5 + 2 = 18/5. Thus, the solution is x = 18/5 and y = 8/5.Rate this question:
-
- 2.
If 3x + 5y = 20 and x = 2, what is the value of y?
- A.
2
- B.
3
- C.
4
- D.
5
Correct Answer
B. 3Explanation
If 3x + 5y = 20 and x = 2, substitute x = 2 into the equation: 3(2) + 5y = 20, which simplifies to 6 + 5y = 20. Subtract 6 from both sides: 5y = 14. Divide by 5 to get y = 14/5. Therefore, the value of y is 14/5 when x = 2.Rate this question:
-
- 3.
Solve for x: 5x - 2y = 10, x = 3, what is y?
- A.
Y = 5
- B.
Y = 2
- C.
Y = 1
- D.
Y = 4
Correct Answer
C. Y = 1Explanation
To solve 5x - 2y = 10, substitute x = 3 into the equation: 5(3) - 2y = 10, simplifying to 15 - 2y = 10.Subtract 15 from both sides: -2y = -5. Divide both sides by -2 to get y = 5/2. Therefore, the value of y is 5/2 when x = 3.Rate this question:
-
- 4.
What is the solution to the system: x + y = 10 and 2x - y = 4?
- A.
X = 6, y = 4
- B.
X = 7, y = 3
- C.
X = 8, y = 2
- D.
X = 9, y = 1
Correct Answer
A. X = 6, y = 4Explanation
The system of equations is x + y = 10 and 2x - y = 4. Solve the first equation for y: y = 10 - x. Substitute this into the second equation: 2x - (10 - x) = 4, which simplifies to 2x - 10 + x = 4. Combining like terms: 3x - 10 = 4. Add 10 to both sides: 3x = 14. Dividing by 3 gives x = 14/3, and substituting into y = 10 - x gives y = 16/3.Rate this question:
-
- 5.
If x + 2y = 10 and y = 3, what is x?
- A.
1
- B.
4
- C.
6
- D.
8
Correct Answer
B. 4Explanation
If x + 2y = 10 and y = 3, substitute y = 3 into the equation: x + 2(3) = 10, simplifying to x + 6 = 10. Subtract 6 from both sides: x = 4. Thus, the value of x is 4 when y = 3.Rate this question:
-
- 6.
What is the solution for 4x - y = 7 and x + y = 5?
- A.
X = 4, y = 1
- B.
X = 3, y = 2
- C.
X = 2, y = 3
- D.
X = 5, y = 0
Correct Answer
B. X = 3, y = 2Explanation
The system 4x - y = 7 and x + y = 5 can be solved by substitution. From the second equation, y = 5 - x. Substitute this into the first equation: 4x - (5 - x) = 7. Simplifying: 4x - 5 + x = 7, which becomes 5x - 5 = 7. Adding 5 to both sides gives 5x = 12. Divide by 5 to get x = 12/5. Substituting into y = 5 - x gives y = 13/5.Rate this question:
-
- 7.
Solve for x: 7x + 2y = 21 and y = 2.
- A.
X = 3
- B.
X = 2
- C.
X = 5
- D.
X = 6
Correct Answer
A. X = 3Explanation
Solve 7x + 2y = 21 and y = 2. Substitute y = 2 into the equation: 7x + 2(2) = 21, simplifying to 7x + 4 = 21. Subtract 4 from both sides: 7x = 17. Divide both sides by 7 to get x = 17/7. Thus, the value of x is 17/7 when y = 2.Rate this question:
-
- 8.
What is the solution for 2x + 5y = 25 and x = 3?
- A.
Y = 2
- B.
Y = 3
- C.
Y = 4
- D.
Y = 5
Correct Answer
B. Y = 3Explanation
For the equation 2x + 5y = 25 and x = 3, substitute x = 3 into the equation: 2(3) + 5y = 25, simplifying to 6 + 5y = 25. Subtract 6 from both sides: 5y = 19. Divide both sides by 5 to get y = 19/5. Therefore, the value of y is 19/5 when x = 3.Rate this question:
-
- 9.
Solve for y in the equation: 3x + 4y = 12, if x = 2.
- A.
Y = 2
- B.
Y = 1
- C.
Y = 3
- D.
Y = 4
Correct Answer
A. Y = 2Explanation
Solve 3x + 4y = 12, given x = 2. Substitute x = 2 into the equation: 3(2) + 4y = 12, simplifying to 6 + 4y = 12. Subtract 6 from both sides: 4y = 6. Divide by 4 to get y = 6/4, which simplifies to y = 3/2. Thus, the value of y is 3/2 when x = 2.Rate this question:
-
- 10.
What is the value of y when 2x + 3y = 12 and x = 4?
- A.
1
- B.
2
- C.
3
- D.
4
Correct Answer
C. 3Explanation
The equation is 2x + 3y = 12 and x = 4. Substitute x = 4 into the equation: 2(4) + 3y = 12, simplifying to 8 + 3y = 12. Subtract 8 from both sides: 3y = 4. Divide by 3 to get y = 4/3. Therefore, the value of y is 4/3 when x = 4.Rate this question:
-
Quiz Review Timeline +
Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.
-
Current Version
-
Mar 21, 2025Quiz Edited by
ProProfs Editorial Team -
Jan 28, 2025Quiz Created by
Hansika
Back to top