Question

Use the graph-and-check method to solve the system of linear equations. $$ \begin{aligned} &y=\frac{1}{2} x+2\\\ &y=-x+5 \end{aligned} $$

Short answer

The solution to the system of equations is the point (2,3).

Step-by-step solution

Plot the first equation

Plot the line of the first equation \(y=\frac{1}{2}x+2\). The slope is \(\frac{1}{2}\) and the y-intercept is 2.

Plot the second equation

Plot the line of the second equation \(y=-x+5\). The slope is -1 and the y-intercept is 5.

Find the Intersection Point

The solution to the system of equations is the point where both lines intersect. By comparing the graphs, it can be observed that the point of intersection is (2,3).