Question

Consider the following pair of equations:

x + y = –2
y = 2x + 10

If the two equations are graphed, at what point do the lines representing the two equations intersect?


(–4, 2)
(4, 2)
(–2, 4)
(2, 4)

Answer 1

The 2 lines will cross at what is called the "point of intersection" It is the (x, y) coordinates that are the same for line one and line two. Since the coordinates are equal, we can set them equal to one another in the equations and solve for the value... Let me show you...

We set the y coordinates equal to one another first. Since they give us one of the y coordinates as y = 2x + 10, we use it in the other equation so we can solve for the x coordinate...

x + y = -2

Since y = 2x + 10 then

x + 2x + 10 = -2
3x + 10 = -2
3x = -12
x = -12/3 = -4

Now that we have a value for the x coordinate, we can substitute it back into one of the equations to solve for the y coordinate...

x + y = -2
-4 + y = -2
y = -2 + 4
y = 2

So you now have the x and y coordinates that are the same for each equation, so that is the point of intersection...

(-4, 2)

Answer 2

Asking the Math Gods...


x=-4
y=2