Question

Here is a system of equations. y=-x+4 y=x-6 Graph the system. Then write its solution. Note that you can also answer "No solution" or "Infinitely many" solutions.​

Answer 1

one solution and that is (5,-1)

Explanation:

Given:

system of equations:

• y=-x+4
• y=x-6

we'll plot the two lines on a coordinate plane to graph

The first equation is y = -x + 4, which represents a line with a slope of -1 (negative) and a y-intercept of 4.

The second equation is y = x - 6, which represents a line with a slope of 1 (positive) and a y-intercept of -6.

Now, let's plot these lines:

Graph of y = -x + 4 (Line 1):

- Find the y-intercept: When x = 0, y = -0 + 4 = 4

- Find another point: When x = 2, y = -2 + 4 = 2

Plot points A(0, 4) and B(2, 2), and draw a straight line passing through them.

Graph of y = x - 6 (Line 2):

- Find the y-intercept: When x = 0, y = 0 - 6 = -6

- Find another point: When x = 2, y = 2 - 6 = -4

Plot the points C(0, -6) and D(2, -4), and draw a straight line passing through them.

The solution to this system of equations is the point where the two lines intersect.

From the graph, you can see that the two lines intersect at point (5, -1).

Therefore, the solution to the system of equations is x = 5 and y = -1.

So the solution is:

x = 5

y = -1

It has one solution and that is (5,-1)

For Graph: Attachment

`\boxed{\textsf{Hope This Helps !!!}}`