Solve the pair of linear equations by addition. $\begin{array} { l }
- 3 x + 2 y = 8 \
- 4 x - 2 y = 6
\end{array}$ 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) $( - 2,1 )$
B) $( 3,1 )$
C) $( 2 , - 1 )$
D) The lines are parallel.
E) The lines coincide.

Question

Solve the pair of linear equations by addition. $\begin{array} { l } 
- 3 x + 2 y = 8 \
- 4 x - 2 y = 6
\end{array}$ 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) $( - 2,1 )$
B) $( 3,1 )$
C) $( 2 , - 1 )$
D) The lines are parallel.
E) The lines coincide.

Quizplus · Accepted Answer

To use addition method, we need to add the two equations to eliminate one of the variables.
Adding the two equations, we get:
\begin{align*}
(-3x + 2y)+(-4x-2y)&=8+6\
-7x&=14\
x&=-2
\end{align*}
Now we can substitute $x=-2$ into either equation and solve for $y$. Using the first equation, we get:
\begin{align*}
-3x+2y&=8\
-3(-2)+2y&=8\
6+2y&=8\
2y&=2\
y&=1
\end{align*}
Therefore, the solution is $(x,y)=(-2,1)$, which corresponds to choice A.

Solve the Pair of Linear Equations by Addition −3x+2y=8−4x−2y=6\begin{array} { l } - 3 x + 2 y = 8 \\- 4 x - 2 y = 6\end{array}−3x+2y=8−4x−2y=6​

Solve the Pair of Linear Equations by Addition $\begin{array} { l } - 3 x + 2 y = 8 \\- 4 x - 2 y = 6\end{array}$