How to work this problem out

Question

x-3y=6.  3x=6y+18

Answer 1

Hello Candy,

 

There are two main ways to go about solving a system of equations like this: through substitution or elimination.  Let's use the substitution method in this case.

 

x-3y=6. 3x=6y+18

 

We need to isolate one of the variables in one of the equations.  You can choose either variable and either equation, whichever you think looks easier.  I will solve for x in the first equation.

 

x-3y=6

x=3y+6

 

Now that I know that x is the same as 3y+6, I can substitute x for 3y+6 in the second equation.

 

3x=6y+18

3(3y+6)=6y+18

 

Now we just need to simplify and solve for y.

 

9y+18=6y+18

3y+18=18

3y=0

y=0

 

We now know that y is 0.  We can plug it back into either of the original equations.  Let's use the first one again.

x-3y=6

x-3(0)=6

x=6

 

So we know that x=6 and that y=0.  Therefore the solution for (x,y) is (6,0).  You can also check the answer by plugging in these values in for x and y in the original equations.  They should both come out as a number equals itself if your answer is correct.

 

If you have any further questions, or if you would like some additional help, I am also available for online tutoring sessions.

Answer 2

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Answer 3

Candy,

 

What is the question you're trying to answer?

 

e.g., are the lines parallel, perpendicular, what (x,y) coordinate solves both?

 

Perhaps you could add that information to help us.