Question

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)

Answer 1

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.