# How do you solve #y+6=2x# & #4x-10y=4#?

##### 2 Answers

#### Explanation:

Strategy: Solve for

Step 1. Solve for

*given*

*subtract 6 from both sides*

Step 2. Plug this

*; given*

*; replace variable #y# with #2x-6#*

*; distribute*#-10# through

*; combine*#x# terms and subtract #60# both sides

*; divide both sides by*#-16 and reduce#

Step 3. Plug this solution back into the equation of step 1.

*; final part of step 1*

*; solution for #x# in step 2*

So your solution is

#### Explanation:

#color(red)(y)+6=2xto(1)#

#4x-10color(red)(y)=4to(2)#

#"note that in " (1)" y can be expressed in terms of x"#

#rArrcolor(red)(y)=2x-6to(3)#

#"substitute into " (2)#

#rArr4x-10(2x-6)=4#

#rArr4x-20x+60=4larr" distributing"#

#rArr-16x+60=4larr" simplifying left side"#

#"subtract 60 from both sides"#

#-16xcancel(+60)cancel(-60)=4-60#

#rArr-16x=-56#

#"divide both sides by - 16"#

#(cancel(-16) x)/cancel(-16)=(-56)/(-16)#

#rArrx=56/16=7/2#

#"substitute this value in " (3)" and evaluate for y"#

#y=(2xx7/2)-6=7-6=1#

#(7/2,1)" is the point of intersection of the 2 equations"#

graph{(y-2x+6)(y-2/5x+2/5)=0 [-10, 10, -5, 5]}