SOLUTION: Use Subtraction to solve each system of equations.If the system does not have exactly one solution, state whether it has no solution or infinitely many solutions. x-3y=0 & 3x+y=

Click here to see ALL problems on Equations

Question 181380: Use Subtraction to solve each system of equations.If the system does not have exactly one solution, state whether it has no solution or infinitely many solutions. x-3y=0 & 3x+y=7
Answer by eperette(173) (Show Source):
You can put this solution on YOUR website!
x-3y=0
3x+y=7
****************
YOU WANT TO HAVE THE SAME NUMBER OF X'S AT TOP AS THE BOTTOM OR THE SAME NUMBER OF Y'S AT TOP AS THE BOTTOM...I WILL DEMOSTRATE WITH X'S
************
3(x - 3y = 0)
3x + y = 7
****************
3x - 9y = 0
3x + y = 7
***************
now we can subtract the bottom equation from top to get rid of the x's
(3x - 9y = 0)
-(3x + y = 7)
***********************
0x - 10y = -7
-10y/-10 = -7/-10
y = 7/10
***********************
go back and substitute to find into any complete equation...
x - 3y = 0
x - 3(7/10) = 0
x - 21/10 = 0
x -21/10 + 21/10 = 0 + 21/10
x + 0 = 21/10
x = 21/10
**********************
so your answer is the coordinate point (21/10, 7/10)
**********************
LETS CHECK:
x-3y=0
21/10 - 3(7/10)
21/10 - 21/10
0 good
3x+y=7
3(21/10) + 7/10
63/10 + 7/10
70/10
7 good