Question Watch Video Show Examples A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 30 pounds and each large box of paper weighs 60 pounds. A total of 26 boxes of paper were shipped weighing 1200 pounds altogether. Graphically solve a system of equations in order to determine the number of small boxes shipped, $x$, and the number of large boxes shipped, $y$.

Step 1 ：Set up two equations based on the information given in the problem. The first equation comes from the total number of boxes: \(x + y = 26\)

Step 2 ：The second equation comes from the total weight of the boxes: \(30x + 60y = 1200\)

Step 3 ：Simplify the second equation by dividing everything by 10: \(3x + 6y = 120\)

Step 4 ：Further simplify it by dividing everything by 3: \(x + 2y = 40\)

Step 5 ：Now we have two equations: \(x + y = 26\) and \(x + 2y = 40\)

Step 6 ：To graphically solve this system of equations, plot these two lines on a graph and find their intersection point.

Step 7 ：The first line (\(x + y = 26\)) will intersect the y-axis at \(y = 26\) (when \(x = 0\)) and the x-axis at \(x = 26\) (when \(y = 0\)).

Step 8 ：The second line (\(x + 2y = 40\)) will intersect the y-axis at \(y = 20\) (when \(x = 0\)) and the x-axis at \(x = 40\) (when \(y = 0\)).

Step 9 ：By plotting these two lines on a graph, we can see that they intersect at the point (14, 12).

Step 10 ：Therefore, the solution to the system of equations is \(x = 14\) and \(y = 12\).

Step 11 ：This means that the paper company shipped 14 small boxes and 12 large boxes.

Step 12 ：To check our solution, we can substitute these values back into the original equations: \(14 + 12 = 26\) (which is true) and \(30*14 + 60*12 = 1200\) (which is also true).

Step 13 ：Therefore, our solution is correct. The final answer is \(\boxed{x = 14, y = 12}\)