Solve the system of equations by the substitution method.
-$\left\{ \begin{array} { l }
- 6 y = x + 4 \
4 x + 5 y = 3
\end{array} \right.$
A) $( - 2,0 )$
B) no solution
C) $( 2 , - 1 )$
D) $( 1,0 )$

Question

Solve the system of equations by the substitution method.
-$\left\{ \begin{array} { l } 
- 6 y = x + 4 \
4 x + 5 y = 3
\end{array} \right.$
A) $( - 2,0 )$
B) no solution
C) $( 2 , - 1 )$
D) $( 1,0 )$

Quizplus · Accepted Answer

From the first equation, we can express $x$ in terms of $y$: $x = -6y - 4$. Substituting this expression for $x$ in the second equation gives $4(-6y - 4) + 5y = 3$, which simplifies to $-24y - 16 + 5y = 3$, or $-19y = 19$, leading to $y = -1$. Substituting $y = -1$ back into the expression for $x$ gives $x = -6(-1) - 4 = 2$. Therefore, the solution is $(2, -1)$.

Solve the System of Equations by the Substitution Method {−6y=x+44x+5y=3\left\{ \begin{array} { l } - 6 y = x + 4 \\4 x + 5 y = 3\end{array} \right.{−6y=x+44x+5y=3​

Solve the System of Equations by the Substitution Method $\left\{ \begin{array} { l } - 6 y = x + 4 \\4 x + 5 y = 3\end{array} \right.$