Question

Given the following system of equations, identify the type of system.

x + y = 4 x - y = 6
A.consistent
B.inconsistent
C.equivalent

Answer 1

The system of equations x + y = 4 and x - y = 6 is consistent because there is a unique solution (x = 5, y = -1) that satisfies both equations. Option a.

Step-by-step explanation:

The system of equations provided is x + y = 4 and x - y = 6. To determine the type of system, we can analyze the equations. Both equations are in the form of linear equations, which typically have a single solution if the lines they represent have different slopes, making the system consistent. This means that there exists a unique pair (x, y) that satisfies both equations.

To identify the system's type, we will solve the system. Adding the two equations, we get:

2x = 10

By dividing both sides by 2, we find x = 5. Substituting x back into the first equation (x + y = 4) gives y = -1. Because we found a unique solution (x = 5, y = -1), the system is consistent.

Answer 2

`\underline{+\left\{\begin{array}{ccc}x+y=4\\x-y=6\end{array}\right}\ \ \ |\text{add both sides of equations}\\.\ \ \ \ \ 2x=10\ \ \ |:2\\.\ \ \ \ \ x=5\\\\Answer:\ A.\ consistent`

Because, the system of equations has one solution (a pair of numbers).