How do you solve the following system: #-2x + 5y = 20, 2x-y=7 #?

1 Answer
May 23, 2017

Answer:

#(55/8,27/4)#

Explanation:

#color(red)(-2x)+5y=20to(1)#

#color(red)(2x)-y=7to(2)#

#" the system is probably best solved using "color(blue)"elimination method"#

#"since the x terms have the same numeric value but with"#
#"opposing signs, adding them will eliminate the x term"#

#(1)+(2)" term by term"#

#(-2x+2x)+(5y-y)=(20+7)#

#rArr4y=27#

#"divide both sides by 4"#

#(cancel(4) y)/cancel(4)=27/4#

#rArry=27/4#

#"substitute this value into either " (1)" or " (2)#

#2x-27/4=7larr" substituting in " (2)#

#rArr2x=7+27/4=55/4#

#rArrx=55/8#

#color(blue)"As a check"#

Substitute these values in ( 1 )

#-2(55/8)+5(27/4)=-55/4+135/4=20rarr" True"#

#rArr"point of intersection" =(55/8,27/4)#