Question

Solve the following pair of linear equations for \(x\) and \(y\) algebraically:
\(x + 2y = 9 \quad \text{and} \quad y - 2x = 2\)

Answer 1

Step 1: Express \( x \) in terms of \( y \) from the first equation:

Given \( x + 2y = 9 \), isolate \( x \): \[ x = 9 - 2y \]

Step 2: Substitute this expression for \( x \) into the second equation:

Substitute \( x = 9 - 2y \) into \( y - 2x = 2 \): \[ y - 2(9 - 2y) = 2 \] Simplify: \[ y - 18 + 4y = 2 \] \[ 5y - 18 = 2 \] Solve for \( y \): \[ 5y = 20 \quad \Rightarrow \quad y = 4 \]

Step 3: Substitute \( y = 4 \) into the expression for \( x \):

Substitute \( y = 4 \) into \( x = 9 - 2y \): \[ x = 9 - 2(4) = 9 - 8 = 1 \]

Step 4: Conclusion:

The solution is \( x = 1 \) and \( y = 4 \).