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

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Question: Solve the system of equations: 2x + 3y = 6 and x - y = 1. 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 + 1. Substitute into the first equation: 2(y + 1) + 3y = 6. Simplifying gives 2y + 2 + 3y = 6, or 5y + 2 = 6. Thus, 5y = 4, so y = 0.8. Therefore, x = 0.8 + 1 = 1.8.

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

Practice Questions

Q1
Solve the system of equations: 2x + 3y = 6 and x - y = 1. 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 = 1. What is the value of x?
  • Step 1: Write down the two equations: 2x + 3y = 6 and x - y = 1.
  • Step 2: From the second equation (x - y = 1), solve for x. Add y to both sides: x = y + 1.
  • Step 3: Substitute the expression for x (y + 1) into the first equation (2x + 3y = 6).
  • Step 4: Replace x in the first equation: 2(y + 1) + 3y = 6.
  • Step 5: Distribute 2 in the equation: 2y + 2 + 3y = 6.
  • Step 6: Combine like terms (2y + 3y): 5y + 2 = 6.
  • Step 7: Subtract 2 from both sides: 5y = 4.
  • Step 8: Divide both sides by 5 to solve for y: y = 4/5 = 0.8.
  • Step 9: Now that we have y, substitute it back into the equation x = y + 1 to find x: x = 0.8 + 1.
  • Step 10: Calculate x: x = 1.8.
  • Systems of Equations – The question tests the ability to solve a system of linear equations using substitution.
  • 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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