Solve the pair of linear equations by addition. $\begin{array} { c }
2 x - y = 2 \
3 x + y = 3
\end{array}$ 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) $( 2,0 )$
B) $( 2 , - 2 )$
C) $( 1,0 )$
D) The lines are parallel.
E) The lines coincide.

Question

Solve the pair of linear equations by addition. $\begin{array} { c } 
2 x - y = 2 \
3 x + y = 3
\end{array}$ 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) $( 2,0 )$
B) $( 2 , - 2 )$
C) $( 1,0 )$
D) The lines are parallel.
E) The lines coincide.

Quizplus · Accepted Answer

To solve the pair of equations, we add the two equations together. This will cancel out the y's and allow us to solve for x. Adding the two equations gives us 5x = 5, which means x = 1. Substituting x = 1 into either original equation gives us y = -1. Therefore, the point of intersection is (1, -1), which corresponds to choice C.

Solve the Pair of Linear Equations by Addition 2x−y=23x+y=3\begin{array} { c } 2 x - y = 2 \\3 x + y = 3\end{array}2x−y=23x+y=3​

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