SOLUTION: Solve the system by substitution: x= 3y+6 2x+y= -16 what is x and y?

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Question 182101This question is from textbook Saxon
: Solve the system by substitution:
x= 3y+6
2x+y= -16
what is x and y? This question is from textbook Saxon

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system

x=3y%2B6
2x%2By=-16




2%283y%2B6%29%2By=-16 Plug in x=3y%2B6 into the second equation. In other words, replace each x with 3y%2B6. Notice we've eliminated the x variables. So we now have a simple equation with one unknown.


6y%2B12%2By=-16 Distribute


7y%2B12=-16 Combine like terms on the left side


7y=-16-12Subtract 12 from both sides


7y=-28 Combine like terms on the right side


y=%28-28%29%2F%287%29 Divide both sides by 7 to isolate y



y=-4 Divide




Now that we know that y=-4, we can plug this into x=3y%2B6 to find x



x=3%28-4%29%2B6 Substitute -4 for each y


x=-12%2B6 Multiply


x=-6 Add


So the solutions are x=-6 and y=-4 which form the ordered pair



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+-10%2C+10%2C+-10%2C+10%2C+%28x-6%29%2F3%2C+%28-16-2x%29%2F1%29+ Graph of x=3y%2B6 (red) and 2x%2By=-16 (green)