Solve the system of equations by the substitution method.
-$\left\{ \begin{array} { l }
- 3 x + y = 28 \
- 4 x + 7 y = 77
\end{array} \right.$
A)(-7, 7)
B)(7, -7)
C)(-6, 6)
D)no solution

Question

Solve the system of equations by the substitution method.
-$\left\{ \begin{array} { l } 
- 3 x + y = 28 \
- 4 x + 7 y = 77
\end{array} \right.$
A)(-7, 7)
B)(7, -7)
C)(-6, 6)
D)no solution

Quizplus · Accepted Answer

To solve the system by substitution, first solve one of the equations for one variable in terms of the other. From the first equation, $y = 3x + 28$. Substitute $y$ in the second equation: $-4x + 7(3x + 28) = 77$. Simplify and solve for $x$: $-4x + 21x + 196 = 77$, which simplifies to $17x = -119$, so $x = -7$. Substitute $x = -7$ back into $y = 3x + 28$ to find $y = 3(-7) + 28 = -21 + 28 = 7$. Thus, the solution is $(-7, 7)$.

Solve the System of Equations by the Substitution Method {−3x+y=28−4x+7y=77\left\{ \begin{array} { l } - 3 x + y = 28 \\- 4 x + 7 y = 77\end{array} \right.{−3x+y=28−4x+7y=77​

Solve the System of Equations by the Substitution Method $\left\{ \begin{array} { l } - 3 x + y = 28 \\- 4 x + 7 y = 77\end{array} \right.$