How do you solve the following system: #-2x + 5y = 20, 2x-y=7 #?
1 Answer
May 23, 2017
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)#
