Question

Graph the linear system and tell how many solutions it has. If there is exactly one solution, estimate the solution and check it algebraically.

Answer 1

First you can rewrite the equations to be in the form y = mx + b

Then to graph the equations, you can either just use the y intercept and slope (like I did) or you can make a table of values. (This mainly depend on how your teacher wants you to do it).

Then, you can see there is one solution. I estimated it to be at the point (3,1). Then, I plugged this point into the two equations (and set them to equal each other) then solved.

They were both equal to zero, which confirms that (3,1), or x = 3, is a solution.

Answer 2

There is exactly one solution: (3, 1)

Explanation:

To graph these equations, you need to change them to slope intercept form:

x + y = 4 in slope intercept form is y = -x + 4 (subtract x frok both sides).

x - y = 2 in slope intercept form is y = x - 2 (subtract x from both sides then divide both sides by -1)*.

Now, all you have to do is graph both and find the point they cross at (the solution) which is (3, 1).

* = y can never be negative, which is why you divide by a -1 after subtracting x.

Hope this helps!