Question

The solution of \( x - 2y = 0 \) and \( 3x + 4y - 20 = 0 \) is:

• A. \( x = 2, y = 4 \)
• B. \( x = 4, y = 2 \)
• C. \( x = -2, y = 4 \)
• D. \( x = 2, y = -4 \)

Hint:

To solve a system of linear equations, substitute the expression for one variable into the other equation to solve for the remaining variable.

Answer 1

The Correct Option is A

We are given the system of linear equations: \[ x - 2y = 0 \quad \text{(Equation 1)} \] \[ 3x + 4y - 20 = 0 \quad \text{(Equation 2)} \] Step 1: Solve Equation 1 for \( x \).
From Equation 1, we have: \[ x = 2y \] Substitute this into Equation 2. Step 2: Substituting into Equation 2.
Substitute \( x = 2y \) into Equation 2: \[ 3(2y) + 4y - 20 = 0 \] \[ 6y + 4y - 20 = 0 \] \[ 10y - 20 = 0 \] Step 3: Solving for \( y \).
\[ 10y = 20 \] \[ y = 2 \] Step 4: Solve for \( x \).
Substitute \( y = 2 \) into \( x = 2y \): \[ x = 2(2) = 4 \] Step 5: Conclusion.
Thus, the solution to the system of equations is \( x = 4, y = 2 \).