SOLUTION: Solve the system of equations by the substitution method. y=6x+8 y=9x+10 The solution is: (Type an ordered pair. Type integers or simplified fractions. Ty

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve the system of equations by the substitution method. y=6x+8 y=9x+10 The solution is: (Type an ordered pair. Type integers or simplified fractions. Ty      Log On


   

Question 131039: Solve the system of equations by the substitution method.
y=6x+8
y=9x+10

The solution is:
(Type an ordered pair. Type integers or simplified fractions. Type N if there is no solution. Type I if there are infinitely many solutions.)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system
y=6x%2B8
y=9x%2B10



9x%2B10=6x%2B8 Plug in y=9x%2B10 into the first equation. In other words, replace each y with 9x%2B10. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.




9x=6x%2B8-10 Subtract 10 from both sides


9x-6x=8-10 Subtract 6x from both sides


3x=8-10 Combine like terms on the left side


3x=-2 Combine like terms on the right side


x=%28-2%29%2F%283%29 Divide both sides by 3 to isolate x






Now that we know that x=-2%2F3, we can plug this into y=9x%2B10 to find y



y=9%28-2%2F3%29%2B10 Substitute -2%2F3 for each x


y=4 Simplify


So our answer is x=-2%2F3 and y=4 which also looks like



Notice if we graph the two equations, we can see that their intersection is at . So this verifies our answer.


+graph%28+500%2C+500%2C+-5%2C+5%2C+-5%2C+5%2C+6x%2B8%2C+9x%2B10%29+ Graph of y=6x%2B8 (red) and y=9x%2B10 (green)