solve the system of equations by graphing. then classify the system as consistent or inconsistent and the equations as dependent or independent.
3u+v=13
3u=v+29
What is the solution of the system of equations?
Hey, you should be getting to be abke to do these.
subtract the second equation from the first to get rid of u
3 u + v - 3 u = 13 - v - 29
v = - v - 16
2 v = -16
v = -8
then
3 u -8 = 13
3 u = 21
u = 7
Solve the following system of equations by graphing. If the system is inconsistent or the equations are dependent, say so.
8 x minus 4 y equals8x−4y=
1616
2 x2x=+4
To solve the system of equations by graphing, we need to plot the graphs of both equations on the coordinate plane and find the point of intersection. The coordinates of this point will represent the solution of the system.
Let's first solve the equations individually to find their slope-intercept forms:
1) Equation 1: 3u + v = 13
Rearrange the equation to isolate v:
v = 13 - 3u
2) Equation 2: 3u = v + 29
Rearrange the equation to isolate v:
v = 3u - 29
Now we have the equations in slope-intercept form. Let's plot them on a graph:
For equation 1:
1. Select a range of u-values, such as -10 to 10.
2. Substitute different u-values into the equation to find corresponding v-values.
3. Plot the points (u, v) on the graph.
For equation 2:
1. Use the same range of u-values as before.
2. Substitute different u-values into the equation to find corresponding v-values.
3. Plot the points (u, v) on the graph.
After plotting both equations, look for the point(s) where the graphs intersect. This point represents the solution to the system of equations.
To classify the system as consistent or inconsistent and the equations as dependent or independent, we need to check the relationship between the lines on the graph.
If the lines intersect at a single point, the system is consistent, and the equations are independent.
If the lines are parallel and never intersect, the system is inconsistent, and the equations are independent.
If the lines lie on top of each other, they are the same equation, and the system is consistent. In this case, the equations are dependent.
Once you graph the equations, you can find the solution by identifying the point of intersection.