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Find the values of x and y from the equations: 4x + 5y = 20 and 2x - y = 3. What

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Question: Find the values of x and y from the equations: 4x + 5y = 20 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 second equation, y = 2x - 3. Substituting into the first gives 4x + 5(2x - 3) = 20. Simplifying leads to 4x + 10x - 15 = 20, thus 14x = 35, so x = 2.5.

Find the values of x and y from the equations: 4x + 5y = 20 and 2x - y = 3. What

Practice Questions

Q1
Find the values of x and y from the equations: 4x + 5y = 20 and 2x - y = 3. What is the value of x?
  1. 1
  2. 2
  3. 3
  4. 4

Questions & Step-by-Step Solutions

Find the values of x and y from the equations: 4x + 5y = 20 and 2x - y = 3. What is the value of x?
  • Step 1: Start with the two equations: 4x + 5y = 20 and 2x - y = 3.
  • Step 2: Rearrange the second equation (2x - y = 3) to solve for y. This gives us y = 2x - 3.
  • Step 3: Substitute the expression for y (from Step 2) into the first equation (4x + 5y = 20).
  • Step 4: Replace y in the first equation: 4x + 5(2x - 3) = 20.
  • Step 5: Distribute 5 in the equation: 4x + 10x - 15 = 20.
  • Step 6: Combine like terms (4x + 10x) to get 14x - 15 = 20.
  • Step 7: Add 15 to both sides of the equation: 14x = 35.
  • Step 8: Divide both sides by 14 to solve for x: x = 35 / 14.
  • Step 9: Simplify 35 / 14 to get x = 2.5.
  • Systems of Linear 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.
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