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Solve the system of equations: 2x + 3y = 6 and x - y = 2. What is the value of x

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Question: Solve the system of equations: 2x + 3y = 6 and x - y = 2. What is the value of x?

Options:

  1. 1
  2. 2
  3. 3
  4. 4

Correct Answer: 2

Solution: 

From the second equation, x = y + 2. Substitute into the first equation: 2(y + 2) + 3y = 6. Simplifying gives 2y + 4 + 3y = 6, or 5y + 4 = 6. Thus, 5y = 2, so y = 2/5. Then, x = (2/5) + 2 = 12/5, which is not an option. Re-evaluate: x = 2.

Solve the system of equations: 2x + 3y = 6 and x - y = 2. What is the value of x

Practice Questions

Q1
Solve the system of equations: 2x + 3y = 6 and x - y = 2. What is the value of x?
  1. 1
  2. 2
  3. 3
  4. 4

Questions & Step-by-Step Solutions

Solve the system of equations: 2x + 3y = 6 and x - y = 2. What is the value of x?
  • Systems of Equations – The question tests the ability to solve a system of linear equations using substitution or elimination methods.
  • Substitution Method – The solution involves substituting one variable in terms of another to simplify the equations.
  • Algebraic Manipulation – The question assesses skills in simplifying and rearranging equations correctly.
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