Question

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

Short answer

The solution to the system of equations is the point (1, 1).

Step-by-step solution

- Plot the First Equation

The first equation is in slope-intercept form (y = mx + b) with a slope of 2 and a y-intercept of -1. Plot the y-intercept on the y-axis and then use the slope to plot the rest of the graph. With a slope of 2, for each step to the right on the x-axis, go two steps up on the y-axis.

- Plot the Second Equation

Similarly, plot the second equation. It also is in slope-intercept form with a slope of 1 and a y-intercept of 1. Plot the y-intercept on the y-axis then use the slope to plot the rest of the graph. With a slope of 1, for each step right on the x-axis, go one step up on the y-axis.

- Identify the Intersection Point

The solution to the system of equations is the point where the two lines intersect. In this case, the lines intersect at the point (1, 1). This is the solution of the system of equations.