Solve the system of equationds by graphing.
u=v
4u=3v-3
You're going to have to do just that, I'm afraid. Plot U against V on a piece of graph paper, calculator, spreadsheet or whatever; draw the two lines described by those equations, and see where they intersect. I know where that's going to be: it's at the point (-3, -3), but that alone won't count as a correct answer, since you've been asked to draw a graph.
To solve the system of equations by graphing, we need to plot the graphs of both equations on the same coordinate plane and find the point of intersection.
Let's start with the first equation, u = v. This is a linear equation in slope-intercept form, y = x, where y represents u and x represents v. Since the equation is already in this form, we can proceed to plot the graph.
To plot the graph, we can choose any values for v and find the corresponding values for u. Let's choose three pairs of values:
- When v = 0, u = 0 (0, 0).
- When v = 1, u = 1 (1, 1).
- When v = -1, u = -1 (-1, -1).
Plotting these three points on the coordinate plane, we can draw a straight line passing through them. This line represents the graph of the first equation, u = v.
Now let's move on to the second equation, 4u = 3v - 3. We can rewrite this equation in slope-intercept form by isolating u:
u = (3v - 3) / 4
Now we can choose three values for v and find the corresponding values for u. Let's choose the same three values we used for the first equation:
- When v = 0, u = -3/4 (-3/4, 0).
- When v = 1, u = 0 (0, 1).
- When v = -1, u = -3/2 (-3/2, -1).
Plotting these three points on the coordinate plane, we can draw a straight line passing through them. This line represents the graph of the second equation, 4u = 3v - 3.
Now that we have plotted both equations on the same graph, we need to find the point of intersection, where the two lines intersect. This point represents the solution to the system of equations.
Looking at the graph, we can see that the two lines intersect at the point (1, 1), which means the solution to the system of equations is u = 1 and v = 1.
To ensure the accuracy of our solution, we can substitute these values back into the original equations to verify that they satisfy both equations:
- u = v: 1 = 1 (True)
- 4u = 3v - 3: 4(1) = 3(1) - 3 -> 4 = 0 (False)
Since the second equation does not hold true for the solution (1, 1), we conclude that there is no solution to the given system of equations.