LEAP 2025 Grades 3-8 Major Content. Practice it free.

Both equations have slope $2$ but different $y$-intercepts ($3$ and $-1$), so the lines are parallel and the system has no solution.

Rewrite in slope-intercept form: $y = -x + 5$ and $y = 3x - 3$. The slopes $-1$ and $3$ are different, so the lines intersect at exactly one point.

Distribute $\dfrac{1}{3}$: $2x - 3 + 2x = 11$. Combine like terms: $4x - 3 = 11$. Add $3$ to both sides: $4x = 14$. Divide by $4$: $x = \dfrac{7}{2}\textsf{.}$

Subtract $8$ from both sides: $-2y - 8 = 4x$. Divide both sides by $4$: $x = \dfrac{-2y - 8}{4}$.

In $y = mx + b$, the slope is $m = \dfrac{3}{2}$.

Substitute $x = 10$: $10n + 150 = 80$, so $10n = -70$ and $n = -7$. The rule is $t(x) = -7x + 150$, so $t(20) = -7(20) + 150 = -140 + 150 = 10$.

Admission is the starting cost ($\text{\char36}12$) and each ride adds $\text{\char36}3$, so $y = 3x + 12\textsf{.}$

Slope $= \dfrac{8 - 2}{3 - 1} = \dfrac{6}{2} = 3\textsf{.}$