How do you solve y=2x-1 and y=x+2?

1 Answer
Aug 5, 2016

First part of the calculation given in detail so that you can see the method more clearly. The second part uses shortcuts.

Point of intersection P_1->(x,y)=(3,5)

Explanation:

Given:

y=2x-1....................Equation(1)
y=x+2.....................Equation(2)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider equation 2

Subtract color(blue)(2) from both sides

color(brown)(ycolor(blue)(-2)=x+2color(blue)(-2))

y-2=x..........................Equation(3)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Using equation(3) substitute for x in equation(1)

y=2(y-2)-1

y=2y-4-1

y=2y-5

Subtract color(blue)(y) form both sides

color(brown)(ycolor(blue)(-y)=2ycolor(blue)(-y)-5)

0=y-5

Add 5 to both sides

y=5
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Substitute y=5 into either equation(1) or (2). I chose (2)

y=x+2" "->" "5=x+2

x=3

Tony B