Solve the system of equations by the substitution method.
-$$\begin{array} { l }
5 x - 3 y = 49 - 5 x \
3 x + 7 y = x + 6 y + 5
\end{array}$$
A) $\left. \left\{ \int \frac { 49 } { 10 } , 0 \right) \right\}$
B) $\{ ( 4 , - 3 ) \}$
C) $\{ ( 4,3 ) \}$
D) $\{ ( 0,49 ) \}$

Question

Solve the system of equations by the substitution method.
-$$\begin{array} { l } 
5 x - 3 y = 49 - 5 x \
3 x + 7 y = x + 6 y + 5
\end{array}$$
A) $\left. \left\{ \int \frac { 49 } { 10 } , 0 \right) \right\}$
B) $\{ ( 4 , - 3 ) \}$
C) $\{ ( 4,3 ) \}$
D) $\{ ( 0,49 ) \}$

Quizplus · Accepted Answer

First, simplify the first equation to $10x - 3y = 49$. For the second equation, simplify to $2x + y = 5$. Solve the second equation for $y$: $y = 5 - 2x$. Substitute into the first equation: $10x - 3(5 - 2x) = 49$. Simplify to find $x = 4$. Substitute $x = 4$ back into $y = 5 - 2x$ to find $y = -3$. The solution is $(4, -3)$.

Solve the System of Equations by the Substitution Method 5x−3y=49−5x3x+7y=x+6y+5\begin{array} { l } 5 x - 3 y = 49 - 5 x \\3 x + 7 y = x + 6 y + 5\end{array}5x−3y=49−5x3x+7y=x+6y+5​

Solve the System of Equations by the Substitution Method $\begin{array} { l } 5 x - 3 y = 49 - 5 x \\3 x + 7 y = x + 6 y + 5\end{array}$