Answer:

To solve the system of linear equations by graphing, we need to represent each equation as a line in the xy-plane and find the point(s) where the lines intersect.

1. To represent the first equation as a line, we can write it in slope-intercept form: y = (1/4)x + 1. To find the y-intercept, we can plug in x = 0 and solve for y: y = (1/4)0 + 1 = 1. So the equation can be written as y = (1/4)x + 1.

2. To represent the second equation as a line, we can write it in slope-intercept form: y = (1/3)x - 2/3. To find the y-intercept, we can plug in x = 0 and solve for y: y = (1/3)0 - 2/3 = -2/3. So the equation can be written as y = (1/3)x - 2/3.

3. To represent the third equation as a line, we can write it in slope-intercept form: y = (1/3)x + 11/3. To find the y-intercept, we can plug in x = 0 and solve for y: y = (1/3)0 + 11/3 = 11/3. So the equation can be written as y = (1/3)x + 11/3.

To sketch the lines, we can create a grid of coordinates and draw the lines according to their equations. The y-intercepts will be the points where the lines intersect the y-axis, and the slope of the line will determine its angle with the x-axis.

The first equation is the line y = (1/4)x + 1, which has a slope of 1/4 and an y-intercept of 1. The second equation is the line y = (1/3)x - 2/3, which has a slope of 1/3 and a y-intercept of -2/3. The third equation is the line y = (1/3)x + 11/3, which has a slope of 1/3 and an y-intercept of 11/3.