JAMB Mathematics 2019 Paper

Concept:Use substitution to express one variable in terms of the other, then solve the resulting quadratic equation.Explanation:Given $3x + y = 21$ and $xy = 30$.From $xy = 30$, write $y = \frac{30}{x}$, where $x \neq 0$.Substitute this value of $y$ into the first equation:$3x + \frac{30}{x} = 21$.Multiply both sides by $x$ to remove the fraction:$3x^2 + 30 = 21x$.Rearrange to form a quadratic equation:$3x^2 - 21x + 30 = 0$.Divide through by $3$:$x^2 - 7x + 10 = 0$.Factorize the quadratic:$(x - 5)(x - 2) = 0$.So $x = 5$ or $x = 2$.Now find the corresponding $y$ values using $y = \frac{30}{x}$:If $x = 5$, then $y = \frac{30}{5} = 6$.If $x = 2$, then $y = \frac{30}{2} = 15$.Answer:$x = 2$ or $5$, and $y = 15$ or $6$ respectively.