Solve the system by graphing. $\left\{ \begin{array} { l }
x = 2 \
y = - \frac { 1 } { 2 } x + 3
\end{array} \right.$

Question

Solve the system by graphing. $\left\{ \begin{array} { l } 
x = 2 \
y = - \frac { 1 } { 2 } x + 3
\end{array} \right.$

Quizplus · Accepted Answer

The system consists of two linear equations. The first equation, x = 2, is a vertical line passing through x = 2 on the x-axis. The second equation, y = -1/2x + 3, is a line with y-intercept 3 and slope -1/2. To graph it, plot the y-intercept at (0, 3) and use the slope -1/2 to find additional points: move down 1 unit and right 2 units to reach (2, 2), and up 1 unit and left 2 units to reach (-2, 4). Connect the points to get a straight line. The point of intersection of the two lines corresponds to the unique solution of the system, which is (2, 2.5). Alternatively, one can substitute x = 2 from the first equation into the second equation to get y = 2.5, which is the same solution. Therefore, the answer is B.

Solve the System by Graphing {x=2y=−12x+3\left\{ \begin{array} { l } x = 2 \\y = - \frac { 1 } { 2 } x + 3\end{array} \right.{x=2y=−21​x+3​

Solve the System by Graphing $\left\{ \begin{array} { l } x = 2 \\y = - \frac { 1 } { 2 } x + 3\end{array} \right.$