Question

A pair of equations is shown below.
X + y = 5
Y = 1/2x + 2
If the two equations are graphed, at what point do the lines representing the two equations intersect?

Answer 1

To find the point of intersection of the two lines, we need to solve the system of equations.

First, substitute the second equation into the first equation:
x + (1/2x + 2) = 5
Combine like terms:
1.5x + 2 = 5
Subtract 2 from both sides:
1.5x = 3
Divide by 1.5:
x = 2

Now that we have the value of x, we can substitute it back into the second equation to find y:
y = (1/2)(2) + 2
y = 1 + 2
y = 3

Therefore, the lines representing the two equations intersect at the point (2, 3).