Solve Linear Systems by Addition
-$$\begin{array} { l }
- 3 x + 7 y = 24 \
- 5 x - 4 y = - 7
\end{array}$$
A) $\{ ( - 1,3 ) \}$
B) $\{ ( 1 , - 3 ) \}$
C) $\{ ( - 1 , - 3 ) \}$
D) $\{ ( 1,3 ) \}$

Question

Solve Linear Systems by Addition
-$$\begin{array} { l } 
- 3 x + 7 y = 24 \
- 5 x - 4 y = - 7
\end{array}$$
A) $\{ ( - 1,3 ) \}$
B) $\{ ( 1 , - 3 ) \}$
C) $\{ ( - 1 , - 3 ) \}$
D) $\{ ( 1,3 ) \}$

Quizplus · Accepted Answer

To solve the system of equations by addition, we first aim to eliminate one variable. Multiplying the first equation by 4 and the second by 7 gives us:$$ -12x + 28y = 96 $$$$ -35x - 28y = -49 $$Adding these equations together eliminates $y$, resulting in:$$ -47x = 47 $$Solving for $x$ gives $x = -1$. Substituting $x = -1$ into one of the original equations to solve for $y$ gives $y = 3$. Therefore, the solution is $(-1, 3)$.

Solve Linear Systems by Addition - −3x+7y=24−5x−4y=−7\begin{array} { l } - 3 x + 7 y = 24 \\- 5 x - 4 y = - 7\end{array}−3x+7y=24−5x−4y=−7​

Solve Linear Systems by Addition
- $\begin{array} { l } - 3 x + 7 y = 24 \\- 5 x - 4 y = - 7\end{array}$