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If x + 2y = 10 and 2x - y = 3, what is the value of x?

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Question: If x + 2y = 10 and 2x - y = 3, what is the value of x?

Options:

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

Correct Answer: 3

Solution: 

From the first equation, x = 10 - 2y. Substituting into the second gives 2(10 - 2y) - y = 3, solving gives y = 4, x = 2.

If x + 2y = 10 and 2x - y = 3, what is the value of x?

Practice Questions

Q1
If x + 2y = 10 and 2x - y = 3, what is the value of x?
  1. 1
  2. 2
  3. 3
  4. 4

Questions & Step-by-Step Solutions

If x + 2y = 10 and 2x - y = 3, what is the value of x?
Correct Answer: 2
  • Step 1: Start with the first equation: x + 2y = 10.
  • Step 2: Rearrange the first equation to solve for x: x = 10 - 2y.
  • Step 3: Now take the second equation: 2x - y = 3.
  • Step 4: Substitute the expression for x from Step 2 into the second equation: 2(10 - 2y) - y = 3.
  • Step 5: Simplify the equation: 20 - 4y - y = 3.
  • Step 6: Combine like terms: 20 - 5y = 3.
  • Step 7: Move 20 to the other side: -5y = 3 - 20.
  • Step 8: Simplify the right side: -5y = -17.
  • Step 9: Divide both sides by -5 to solve for y: y = 17/5 or y = 3.4.
  • Step 10: Now substitute y back into the expression for x: x = 10 - 2(3.4).
  • Step 11: Calculate: x = 10 - 6.8 = 3.2.
  • Systems of Linear Equations – The question tests the ability to solve a system of linear equations using substitution.
  • Substitution Method – The question assesses the understanding of substituting one equation into another to find variable values.
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