SOLUTION: Solving Linear Systems: Use substitution to solve the linear system. Then check your solution. x - 2y = 9 1.5x + 0.5y = 6.5 I understand how to solve the first equation

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solving Linear Systems: Use substitution to solve the linear system. Then check your solution. x - 2y = 9 1.5x + 0.5y = 6.5 I understand how to solve the first equation      Log On


   

Question 131556: Solving Linear Systems:
Use substitution to solve the linear system. Then check your solution.
x - 2y = 9
1.5x + 0.5y = 6.5


I understand how to solve the first equation, but I don't understand how to substitute the x answer into the second equation to be able to find the value of y.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
x+-+2y+=+9
1.5x+%2B+0.5y+=+6.5

I presume you took the first equation and did something like x=2y%2B9

All you have to do is replace x in the second equation with 2y + 9 and then solve for y.

cartoon%28red%281.5x%29+%2B+0.5y+=+6.5%2Cred%281.5%282y%2B9%29%29+%2B+0.5y+=+6.5%29

1.5%282y%2B9%29+%2B+0.5y+=+6.5
3y%2B13.5%2B0.5y=6.5
3.5y%2B13.5=6.5
3.5y=6.5-13.5
3.5y=-7
y=-2

Now that you know that y=-2, you can substitute that value into either of the equations so that you can solve for x.

cartoon%28x+-+red%282y%29+=+9%2Cx-red%282%28-2%29%29=9%29
x%2B4=9
x=5

So the solution set is the ordered pair (5,-2).

Check your answer by substitution, the ordered pair coordinates should make both equations true statements:
5-%28-2%29=9,9=9 True
1.5%285%29+%2B+0.5%28-2%29+=+6.5, 7.5-1=6.5, 6.5=6.5 True.

You can also graph both lines to see if they intersect at (5,-2)