# How do you solve this system of equation: #5x - 6y = 9 and 9- 3y = - x#?

##### 1 Answer

Nov 13, 2017

#### Explanation:

#5x-6y=9to(1)#

#9-3y=-xto(2)#

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

#"multiply through by "-1#

#-9+3y=xto(3)#

#color(blue)"substitute "x=3y-9" into equation "(1)#

#5(3y-9)-6y=9#

#rArr15y-45-6y=9#

#rArr9y-45=9#

#"add 45 to both sides"#

#9ycancel(-45)cancel(+45)=9+45#

#rArr9y=54#

#"divide both sides by 9"#

#(cancel(9) y)/cancel(9)=54/9#

#rArry=6#

#"substitute this value into equation "(3)#

#rArrx=-9+(3xx6)=-9+18=9#

#"point of intersection "=(9,6)#

graph{(y-5/6x+3/2)(y-1/3x-3)((x-9)^2+(x-6)^2-0.05)=0 [-20, 20, -10, 10]}