NH SAS Grade 8 Expressions and Equations. Practice it free.

The Negative Exponent Property says that a nonzero base raised to a negative exponent equals the reciprocal of that base raised to the positive exponent, written $a^{-n} = \dfrac{1}{a^{n}}\textsf{.}$ Applying the property, $a^{-2} = \dfrac{1}{a^{2}}\textsf{.}$

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 $4$: $x = \dfrac{-2y - 8}{4}$.

$8 \times 8 = 64$, so $\sqrt{64} = 8$.

The Power of a Product Property says that a product raised to a power equals each factor raised to that power, written $(ab)^{n} = a^{n} \cdot b^{n}\textsf{.}$ Here $(3 \cdot 7)^{4} = 3^{4} \cdot 7^{4}$, so $a = 4\textsf{.}$

Both equations have slope $-3$ but different $y$-intercepts ($2$ and $5$), so the lines are parallel and the system has no solution.