First of all we need to find the equations of the lines :
y( red ) = - x + 2
y(blue) = 2x - 1
Then we must to put the equations equal to each other and going to to find the value of x :
[tex]- x + 2 = 2x - 1[/tex]
Add both sides x
[tex] - x + x + 2 = 2x + x - 1[/tex]
[tex]2 = 3x - 1[/tex]
Add both sides 1
[tex]2 + 1 = 3x - 1 + 1[/tex]
[tex] 3 = 3x[/tex]
Switch sides
[tex]3x = 3[/tex]
Divide both sides by 3
[tex] \frac{3x}{3} = \frac{3}{3} \\ [/tex]
[tex]x = 1[/tex]
After u the value of x , put it in one the equations to find the value of y :
[tex]y = - x + 2[/tex]
[tex]y = - (1) + 2[/tex]
[tex]y = - 1 + 2[/tex]
[tex]y = 1[/tex]
Thus the solution is ( 1 , 1 ) .
