Solve the system by substitution.
-$$\begin{aligned}
x + 2 y & = 10 \
2 x - 7 y & = - 2
\end{aligned}$$
A) $\{ ( 6,2 ) \}$
B) $\left\{ ( x , y ) \mid y = - \frac { 1 } { 2 } x + 5 \right\}$; The equations are dependent
C) $\{ ( 14 , - 2 ) \}$
D) $\{ ( 13,4 ) \}$

Question

Quizplus · Accepted Answer

Solving the first equation for $x$, we get $x = 10 - 2y$. Substituting this into the second equation gives $2(10 - 2y) - 7y = -2$, which simplifies to $20 - 4y - 7y = -2$, or $20 - 11y = -2$, leading to $11y = 22$, so $y = 2$. Substituting $y = 2$ back into $x = 10 - 2y$ gives $x = 10 - 2(2) = 6$. Therefore, the solution is $(6, 2)$.

Solve the System by Substitution x+2y=102x−7y=−2\begin{aligned}x + 2 y & = 10 \\2 x - 7 y & = - 2\end{aligned}x+2y2x−7y​=10=−2​

Solve the System by Substitution $\begin{aligned}x + 2 y & = 10 \\2 x - 7 y & = - 2\end{aligned}$