1. **State the problem:** We are given two equations based on the cost of rackets and squash balls: - The cost of 2 rackets and 3 squash balls is 21.63. - The cost of 5 rackets and 7 squash balls is 52.90. We need to find the cost of one racket and one squash ball. 2. **Define variables:** Let $x$ be the cost of one racket and $y$ be the cost of one squash ball. 3. **Write the system of equations:** $$\begin{cases} 2x + 3y = 21.63 \\ 5x + 7y = 52.90 \end{cases}$$ 4. **Use elimination or substitution to solve.** We will use elimination. Multiply the first equation by 5 and the second by 2 to align the $x$ terms: $$\begin{cases} 5(2x + 3y) = 5(21.63) \\ 2(5x + 7y) = 2(52.90) \end{cases}$$ Which gives: $$\begin{cases} 10x + 15y = 108.15 \\ 10x + 14y = 105.80 \end{cases}$$ 5. **Subtract the second equation from the first:** $$ (10x + 15y) - (10x + 14y) = 108.15 - 105.80 $$ $$ 10x - \cancel{10x} + 15y - 14y = 2.35 $$ $$ y = 2.35 $$ 6. **Substitute $y = 2.35$ into the first original equation:** $$ 2x + 3(2.35) = 21.63 $$ $$ 2x + 7.05 = 21.63 $$ $$ 2x = 21.63 - 7.05 $$ $$ 2x = 14.58 $$ $$ x = \frac{14.58}{2} $$ $$ x = 7.29 $$ 7. **Final answers:** - Cost of one racket $x = 7.29$ - Cost of one squash ball $y = 2.35$