Solve the system of equations by either the addition method or the substitution method.
-$\left\{ \begin{array} { l }
\frac { x + 3 } { 4 } = \frac { y + 19 } { 8 } \
\frac { x } { 3 } = \frac { 2 y + 6 } { 6 }
\end{array} \right.$
A) infinite number of solutions
B) $( 10,7 )$
C) no solution
D) $( 7,10 )$

Question

Solve the system of equations by either the addition method or the substitution method.
-$\left\{ \begin{array} { l } 
\frac { x + 3 } { 4 } = \frac { y + 19 } { 8 } \
\frac { x } { 3 } = \frac { 2 y + 6 } { 6 }
\end{array} \right.$
A) infinite number of solutions
B) $( 10,7 )$
C) no solution
D) $( 7,10 )$

Quizplus · Accepted Answer

First, simplify both equations. For the first equation, multiply both sides by 8 to get $2(x + 3) = y + 19$, which simplifies to $2x - y = 13$. For the second equation, multiply both sides by 6 to get $2x = 2y + 6$, which simplifies to $x - y = 3$. Solving these two equations together, you find that $x = 10$ and $y = 7$, making the solution $(10, 7)$.

Solve the System of Equations by Either the Addition Method {x+34=y+198x3=2y+66\left\{ \begin{array} { l } \frac { x + 3 } { 4 } = \frac { y + 19 } { 8 } \\\frac { x } { 3 } = \frac { 2 y + 6 } { 6 }\end{array} \right.{4x+3​=8y+19​3x​=62y+6​​

Solve the System of Equations by Either the Addition Method $\left\{ \begin{array} { l } \frac { x + 3 } { 4 } = \frac { y + 19 } { 8 } \\\frac { x } { 3 } = \frac { 2 y + 6 } { 6 }\end{array} \right.$