What are the points of intersection for #y = 2x + 3# and #y = x + 5#?
1 Answer
Suppose we separated the variables into
#\mathbf(y_1 = 2x_1 + 3)#
#\mathbf(y_2 = x_2 + 5)#
The point of intersection occurs when the two graphs have equal values of
The solution will be the coordinate
What we can do to proceed is assume that
#2x_1 + 3 = x_2 + 5#
#= x_1 + 5#
Subtract
#x_1 + 3 = 5#
Then I would subtract
#color(blue)(x_1 = x_2 = 2)#
Now, since the solution coordinate requires that we have both
#color(blue)(y_1) = 2x_1 + 3#
#= 2(2) + 3 = color(blue)(7)#
And just to show that indeed
#color(green)(y_2) = x_2 + 5#
#= x_1 + 5#
#= 2 + 5#
#= color(green)(7 = y_1)#
Finally, that means our solution coordinate is:
#color(blue)("("2,7")")#