solve the system of equations by graphing. Then classify the system as consistent or inconsistent and the equations as dependent or independent.
x+y=14
x-y=2
What is the solution of the system of equations?
I can not very well graph them here and see where they hit, but I can add them
2 x + y - y = 14 + 2
2 x = 16
x = 8
then
8 + y = 14
y = 6
so your lines should intersect at (8,6)
re the two functions parallel, perpendicular, the same equation or none of these choices?
4x+4y=8
5x+5y=15
To solve the system of equations by graphing, we will plot the lines represented by each equation and determine the point(s) of intersection.
The first equation, x + y = 14, can be rearranged to y = -x + 14. Using this equation, we can determine two points to plot the line: when x = 0, y = 14, and when y = 0, x = 14.
The second equation, x - y = 2, can be rearranged to y = x - 2. Using this equation, we can determine two points to plot the line: when x = 0, y = -2, and when y = 0, x = 2.
Plotting these lines on a graph, they intersect at the point (8, 6).
Now, to classify the system:
- Since the lines intersect at a single point, the system is consistent.
- The equations are independent because they intersect at a single point, meaning they do not have infinitely many solutions.
Therefore, the solution of the system of equations is x = 8 and y = 6.
To solve the system of equations by graphing, we will first graph each equation on the coordinate plane.
Equation 1: x + y = 14
For this equation, we can rearrange it to solve for y: y = 14 - x.
Now we can plot the points on the coordinate plane. We'll choose a few values for x, plug them into the equation to find y, and plot the points. After connecting these points, we will get a straight line.
Equation 2: x - y = 2
Rearranging this equation, we get: y = x - 2.
Again, we'll choose some x-values, find the corresponding y-values, and plot the points. Connect them to form another straight line.
Once we have graphed both lines, we can see where they intersect, if at all. This point of intersection represents the solution to the system of equations.
To determine if the system is consistent or inconsistent, and if the equations are dependent or independent, we need to consider the number of intersection points.
Solution: By graphing the system, we observe that the lines intersect at the point (8, 6). Hence, the solution to the system of equations is x = 8 and y = 6.
Classification: Since the lines intersect at a unique point, the system is consistent. Furthermore, the equations are independent because they represent two distinct lines.