x+y=6
2x-y=9
Is it a solution?
Why or Why not?
__________________________
(5,1)
______________________
A system of linear equations with the same number of variables and equations only has one solution point (x, y), which is graphically the point of intersection of two lines
__________________
You have two ways to know if it is you replace it in the equations or you solve the system
______________________________
Solving the system
x+y=6 (I)
2x-y=9 (II)
______________
x+y=6 (I)
x= 6-y
Replacing in (II)
2x-y=9 (II)
2(6-y) -y =9
12-2y -y = 9
-3y = 9 -12
y= -3/-3 = 1
y= 1
___________
x= 6- 1
x= 5
_______________
Verifing
x+y=6 (I)
5+ 1= 6
2x-y=9 (II)
2* 5-1=9
9=9
___________
The point (x,y)= (5,1) is the solution of the system of linear equations, x+y=6; 2x-y=9 because the point satisfies the two equalities of the linear equations of the system.
Do you have any questions regarding the solution?
If you don’t need further explanation on this question, we can end the session.
I want to remind you this answer will always be saved in your profile. I’d really appreciate you letting me know how I did by rating our session after you exit. Thanks and have a great day!