Question 3(multiple choice worth 4 points) (08.02)a pair of equations is shown below. x + y = 5 y = x + 2 if the two equations are graphed, at what point do the lines representing the two equations intersect? (2, 5) (5, 2) (2, 3) (3, 2)

The system of linear equations here is   x + y = 5 y = x + 2, better written as

x + y = 5
y = x + 2

Let's solve this system using substitution.  Replace y in the first equaqtion with x+2:  x + (x+2) = 5.  Then 2x + 2 = 5, and it follows that 2x=3.  Solving this equation for x, we get x = 3/2.

Now substitute 3/2 for x in either of the given equations and solve the result for y:  (3/2) + y = 5, or y = 5 - 3/2, or y = (10-3) / 2 = 7/2.

For the given system  x + y = 5 y = x + 2, or 

x + y = 5
y = x + 2, 

the solution is (3/2, 7/2),

This does not match any of the answer choices.  I urge you to go back and ensure that you have copied down the system   x + y = 5     /      y = x + 2  completely and accurately.