# How do you solve the system #x= 3y-1# and #x+2y=9#?

##### 2 Answers

Apr 16, 2018

Arrange the equations. You get

#### Explanation:

(after multiplying the 2nd equation by -1#

Now add these:

Put this value in the 1st original equation:

Apr 16, 2018

#### Explanation:

#x=3y-1to(1)#

#x+2y=9to(2)#

#"rearrange equation "(2)" to give x in terms of y"#

#rArrx=9-2yto(3)#

#"since "(1)" and "(3)" both give x in terms of y we"#

#"can equate the right sides"#

#rArr3y-1=9-2y#

#"add 2y to both sides"#

#3y+2y-1=9cancel(-2y)cancel(+2y)#

#rArr5y-1=9#

#"add 1 to both sides"#

#rArr5y=10rArry=2#

#"substitute "y=2" in either "(1)" or "(3)#

#(1)tox=6-1=5#

#"solution is "(x,y)to(5,2)#