How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #y=4x-1# and #y= -1x + 4#?

Question

Hazel Anglin · Accepted Answer

Consistent with solution set #(1, 3)#.

When we replace, we obtain: #4x - 1= - x + 4# #5x = 5# #x = 1# If follows that #y = 3#. A consistent system of equations is a system that has one real solution (I.E a system with an infinite number or no solutions would be dubbed inconsistent). I hope this is useful!

Eli Assouline · Answer

undefined To solve the system of equations $ y = 4x - 1 $ and $ y = -x + 4 $ by graphing and classify it as consistent or inconsistent:

1. Graph the equations on the same coordinate plane.
2. Determine the point of intersection of the two lines.
3. If the lines intersect at a single point, the system is consistent and has a unique solution at the point of intersection. If the lines are parallel and never intersect, the system is inconsistent and has no solution.

Isaiah Anthony · Answer

undefined To solve the system of equations by graphing:
1. Plot the graph of each equation on the same coordinate system.
2. Identify the point(s) where the two graphs intersect.
3. The coordinates of the intersection point(s) represent the solution(s) to the system.
4. Classify the system as consistent if it has one or more intersection points, or inconsistent if the graphs do not intersect.

For the given equations:
y = 4x - 1
y = -x + 4

Plot the graphs of these equations on the same coordinate system. Then identify the point where they intersect, if any. Finally, determine whether the system is consistent or inconsistent based on the intersection.