Solve the system of equations by the substitution method.
-$$\begin{array} { l }
5 x + 9 y = 41 \
3 x - 4 y = - 13
\end{array}$$
A) $\{ ( 0,5 ) \}$
B) $\{ ( 1,5 ) \}$
C) $\{ ( 1,4 ) \}$
D) $\varnothing$

Question

Solve the system of equations by the substitution method.
-$$\begin{array} { l } 
5 x + 9 y = 41 \
3 x - 4 y = - 13
\end{array}$$
A) $\{ ( 0,5 ) \}$
B) $\{ ( 1,5 ) \}$
C) $\{ ( 1,4 ) \}$
D) $\varnothing$

Quizplus · Accepted Answer

First, solve the second equation for $x$: $3x = 4y - 13$ or $x = \frac{4y - 13}{3}$. Substitute this expression for $x$ in the first equation: $5(\frac{4y - 13}{3}) + 9y = 41$. Simplify and solve for $y$: $20y - 65 + 27y = 123$, leading to $47y = 188$, so $y = 4$. Substitute $y = 4$ back into $x = \frac{4y - 13}{3}$ to find $x = 1$. Thus, the solution is $(1, 4)$.

Solve the System of Equations by the Substitution Method 5x+9y=413x−4y=−13\begin{array} { l } 5 x + 9 y = 41 \\3 x - 4 y = - 13\end{array}5x+9y=413x−4y=−13​

Solve the System of Equations by the Substitution Method $\begin{array} { l } 5 x + 9 y = 41 \\3 x - 4 y = - 13\end{array}$