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)
