How do you solve #3x+y=5# and #2x- y=20# using substitution?

1 Answer
Mar 14, 2018

Answer:

#(x,y)to(5,-10)#

Explanation:

#3x+y=5to(1)#

#2x-y=20to(2)#

#"Rearrange equation "(1)" to express y in terms of x"#

#"subtract 3x from both sides"#

#cancel(3x)cancel(-3x)+y=5-3x#

#rArry=5-3xto(3)#

#color(blue)"Substitute "y=5-3x" in equation "(2)#

#2x-(5-3x)=20#

#rArr2x-5+3x=20#

#rArr5x-5=20#

#"add 5 to both sides"#

#5xcancel(-5)cancel(+5)=20+5#

#rArr5x=25#

#"divide both sides by 5"#

#(cancel(5) x)/cancel(5)=25/5#

#rArrx=5#

#"substitute "x=5" into equation "(3)#

#rArry=5-(3xx5)=-10#

#rArr"solution is "(5,-10)#