Solve Linear Systems by Addition
-$$\begin{array} { l }
3 x + 7 y = 46 \
3 x + 2 y = 56
\end{array}$$
A) $\{ ( 20 , - 2 ) \}$
B) $\{ ( - 20,3 ) \}$
C) $\{ ( - 20,7 ) \}$
D) $\{ ( - 2,20 ) \}$

Question

Solve Linear Systems by Addition
-$$\begin{array} { l } 
3 x + 7 y = 46 \
3 x + 2 y = 56
\end{array}$$
A) $\{ ( 20 , - 2 ) \}$
B) $\{ ( - 20,3 ) \}$
C) $\{ ( - 20,7 ) \}$
D) $\{ ( - 2,20 ) \}$

Quizplus · Accepted Answer

To solve the system by addition, we can subtract the second equation from the first to eliminate $x$: $$(3x + 7y) - (3x + 2y) = 46 - 56$$ which simplifies to $5y = -10$, giving $y = -2$. Substituting $y = -2$ into one of the original equations, for example, the second one: $3x + 2(-2) = 56$, simplifies to $3x - 4 = 56$, and solving for $x$ gives $x = 20$. Therefore, the solution is $(20, -2)$.

Solve Linear Systems by Addition - 3x+7y=463x+2y=56\begin{array} { l } 3 x + 7 y = 46 \\3 x + 2 y = 56\end{array}3x+7y=463x+2y=56​

Solve Linear Systems by Addition
- $\begin{array} { l } 3 x + 7 y = 46 \\3 x + 2 y = 56\end{array}$