Question

Solve the pair of equations \( 8x + 5y = 9 \) and \( 3x + 2y = 4 \) by substitution method.

Hint:

\textbf{Quick Tips for Solving Linear Equations by Substitution:}
\textbf{Step 1:} Solve one equation for one variable in terms of the other.
\textbf{Step 2:} Substitute this expression into the second equation.
\textbf{Step 3:} Solve for the remaining variable.
\textbf{Step 4:} Substitute the obtained value back into the first equation to find the second variable.
\textbf{Step 5:} Always check the solution by substituting it into both original equations.
\textbf{Tip:} Choose the equation where solving for a variable is easiest to simplify calculations.

Answer 1

From \( 3x + 2y = 4 \):
\[ y = \frac{4 - 3x}{2} \] Substituting in \( 8x + 5y = 9 \):
\[ 8x + 5\left(\frac{4 - 3x}{2}\right) = 9 \] \[ 16x + 20 - 15x = 18 \] \[ x = -2 \] Substituting \( x = -2 \) in \( y = \frac{4 - 3x}{2} \):
\[ y = \frac{4 - 3(-2)}{2} = \frac{4 + 6}{2} = 5 \] Thus, \( x = \mathbf{-2}, y = \mathbf{5} \).
Correct Answer: \( x = -2, y = 5 \)