Question

How many solutions does the system of equations have?

2x-y=8
x=y+2
Explain

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine the number of solutions of the system of equations, we need to find the point(s) where the two lines represented by the equations intersect.

Since the second equation is given in terms of x and y, let's rewrite the first equation in terms of x and y as well.

2x - y = 8
y = 2x - 8

Now we have both equations in slope-intercept form.

The slope-intercept form of a line is y = mx + b, where m is the slope of the line and b is the y-intercept.

Comparing the second equation, x = y + 2, with the slope-intercept form, we can see that the slope is 1.

Comparing the first equation, y = 2x - 8, with the slope-intercept form, we can see that the slope is 2.

Since the slopes of the two lines are different, they are not parallel, and they will intersect at a point (x, y).

Now we can find the point of intersection by setting the y-values from both equations equal to each other:

2x - 8 = x

Subtracting x from both sides:

x = 8

Substituting this value of x into the second equation:

y = 8 + 2 = 10

Therefore, the system of equations has one solution, which is (8, 10).