To solve the system of equations using a graphical method, we need to plot the graphs of the two equations and determine the point where they intersect, since that point represents the solution to the system.
First, let's plot the graph of y = 3x - 5. This is a linear equation in slope-intercept form, where the slope is 3 and the y-intercept is -5. To graph it, we can plot two points and draw a line through them.
To find the x-intercept, set y = 0:
0 = 3x - 5
3x = 5
x = 5/3 ≈ 1.67
To find the y-intercept, set x = 0:
y = 3(0) - 5
y = -5
So, we have two points: (0,-5) and (5/3,0). Let's plot them:
Next, let's plot the graph of y = 13x + 3. Again, this is a linear equation in slope-intercept form, where the slope is 13 and the y-intercept is 3. To graph it, we can plot two points and draw a line through them.
To find the x-intercept, set y = 0:
0 = 13x + 3
13x = -3
x = -3/13 ≈ -0.23
To find the y-intercept, set x = 0:
y = 13(0) + 3
y = 3
So, we have two points: (0,3) and (-3/13,0). Let's plot them:
Now, we can see that the two lines intersect at the point (4,3). Therefore, the solution to the system of equations is x = 4 and y = 3.
The correct answer is A) (4, 3).