Question

X + y = 4 x - y = 6 consistent, inconsistent, equivalent

Answer 1

The system of equations x + y = 4 and x - y = 6 has a unique solution (5, -1), making it consistent and independent. Since the slopes are equal and the y-intercepts differ, the equations are not equivalent.

Step-by-step explanation:

To determine whether the system of equations x + y = 4 and x - y = 6 is consistent, inconsistent, or equivalent, we can solve the system by addition or subtraction.

Let's add the two equations:

• x + y = 4
• x - y = 6

Adding the left sides of the equations yields 2x, and adding the right sides gives 10. So, we get:

2x = 10

Dividing both sides by 2 gives us:

x = 5

Now, we can substitute x = 5 into either original equation to solve for y. Substituting into the first equation:

5 + y = 4

y = 4 - 5

y = -1

Therefore, we have a unique solution, (5, -1), which means the system of equations is consistent and independent.

Now, let's examine the system's slope and y-intercept:

• The slope of x + y = 4 is -1 and the y-intercept is 4.
• The slope of x - y = 6 is also -1, but the y-intercept is -6.

The slopes are the same, however, the y-intercepts differ, so these two lines intersect at one point and are not equivalent.

Answer 2

inconsistent maybe???