Solve the pair of linear equations by addition. $\begin{array} { l }
3 x - 2 y = 18 \
3 x + 4 y = 26
\end{array}$ If there is one common solution, select the correct ordered pair of the point of intersection. If there is no one common solution, select either parallel or coincide for the correct answer.
A) $\left( 6 \frac { 8 } { 9 } , 1 \frac { 1 } { 3 } \right)$
B) $\left( 4 , - 1 \frac { 1 } { 3 } \right)$
C) $\left( 3 \frac { 8 } { 9 } , 4 \frac { 1 } { 3 } \right)$
D) The lines are parallel.
E) The lines coincide.

Question

Solve the pair of linear equations by addition. $\begin{array} { l } 
3 x - 2 y = 18 \
3 x + 4 y = 26
\end{array}$ If there is one common solution, select the correct ordered pair of the point of intersection. If there is no one common solution, select either parallel or coincide for the correct answer.
A) $\left( 6 \frac { 8 } { 9 } , 1 \frac { 1 } { 3 } \right)$
B) $\left( 4 , - 1 \frac { 1 } { 3 } \right)$
C) $\left( 3 \frac { 8 } { 9 } , 4 \frac { 1 } { 3 } \right)$
D) The lines are parallel.
E) The lines coincide.

Quizplus · Accepted Answer

By subtracting the first equation from the second, we eliminate $3x$ and solve for $y$, finding $y = \frac{4}{3}$. Substituting back, we find $x = \frac{62}{9}$, which matches option A.

Solve the Pair of Linear Equations by Addition 3x−2y=183x+4y=26\begin{array} { l } 3 x - 2 y = 18 \\3 x + 4 y = 26\end{array}3x−2y=183x+4y=26​

Solve the Pair of Linear Equations by Addition $\begin{array} { l } 3 x - 2 y = 18 \\3 x + 4 y = 26\end{array}$