Question

Solve the following pair of linear equations:
\( 0.2x + 0.3y = 1.3 \) and \( 0.4x - 0.5y = -0.7 \).

Hint:

Always remove decimals first when solving equations — it simplifies calculations and reduces chances of error.

Answer 1

Step 1: Eliminate decimals for simplicity.
Multiply both equations by 10: \[ 2x + 3y = 13 \quad \text{(i)} \] \[ 4x - 5y = -7 \quad \text{(ii)} \]
Step 2: Use the elimination method.
Multiply (i) by 2 to make the coefficients of \( x \) equal: \[ 4x + 6y = 26 \quad \text{(iii)} \] Now subtract (ii) from (iii): \[ (4x + 6y) - (4x - 5y) = 26 - (-7) \] \[ 4x + 6y - 4x + 5y = 33 \] \[ 11y = 33 \Rightarrow y = 3 \]
Step 3: Substitute \( y = 3 \) in equation (i).
\[ 2x + 3(3) = 13 \] \[ 2x + 9 = 13 \Rightarrow 2x = 4 \Rightarrow x = 2 \]
Step 4: Conclusion.
Hence, the solution of the given pair of linear equations is \[ \boxed{x = 2, \; y = 3} \]