Question

Find the solution to the system of equations by graphing
Y=2x - 1 and y=x + 3

Answer 1

To graph the system of equations, first plot the y-intercept for each equation.

For the first equation, y = 2x - 1, the y-intercept is -1. Plot the point (0, -1).

For the second equation, y = x + 3, the y-intercept is 3. Plot the point (0, 3).

Next, find the slope for each equation.

The slope for the first equation, y = 2x - 1, is 2. This means that for every 1 unit increase in x, the corresponding y-value increases by 2.

The slope for the second equation, y = x + 3, is 1. This means that for every 1 unit increase in x, the corresponding y-value increases by 1.

Plot the slope by moving up 2 units and over 1 unit from the first point. Then plot the slope by moving up 1 unit and over 1 unit from the second point. Repeat this process to plot additional points.

The graph of the two equations should intersect at a single point. This point represents the solution to the system of equations.