Solve the system by the substitution method.
-$$\left\{ \begin{array} { l }
5 x + 3 y = 80 \
2 x + y = 30
\end{array} \right.$$
A) $\{ ( x , y ) \mid 2 x + y = 30 \}$
B) $\{ ( 10,10 ) \}$
C) $\varnothing$
D) $\{ ( 0,10 ) \}$

Question

Solve the system by the substitution method.
-$$\left\{ \begin{array} { l } 
5 x + 3 y = 80 \
2 x + y = 30
\end{array} \right.$$
A) $\{ ( x , y ) \mid 2 x + y = 30 \}$
B) $\{ ( 10,10 ) \}$
C) $\varnothing$
D) $\{ ( 0,10 ) \}$

Quizplus · Accepted Answer

To solve the system by substitution, we first solve one of the equations for one variable in terms of the other. From the second equation, $2x + y = 30$, we can solve for $y$ to get $y = 30 - 2x$. Substituting this expression for $y$ in the first equation, $5x + 3(30 - 2x) = 80$, simplifies to $5x + 90 - 6x = 80$, which further simplifies to $-x = -10$, giving $x = 10$. Substituting $x = 10$ back into the equation $y = 30 - 2x$ gives $y = 30 - 2(10) = 10$. Therefore, the solution to the system is $(x, y) = (10, 10)$.

Solve the System by the Substitution Method {5x+3y=802x+y=30\left\{ \begin{array} { l } 5 x + 3 y = 80 \\2 x + y = 30\end{array} \right.{5x+3y=802x+y=30​

Solve the System by the Substitution Method $\left\{ \begin{array} { l } 5 x + 3 y = 80 \\2 x + y = 30\end{array} \right.$