How do solve the following linear system?: # -2x+5y=-3, x-3y=-2 #?

1 Answer
Mar 13, 2016

Answer:

#(x,y)=(19,7)#

Explanation:

Solve by elimination and substitution

#1)color(blue)(-2x+5y=-3#

#2)color(blue)(x-3y=-2#

If you see carefully, you could eliminate #-2x# from the first equation by #x# in the second equation if we multiply #x# with #2# to get #2x#

#rarr2(x-3y=-2)#

Use distributive property #color(brown)(a(b+c=d),ab+ac=ad#

#rarr2x-6y=-4#

Now, add both of the equations

#rarr(-2x+5y=-3)+(2x-6y=-4)#

#rarr-y=-7#

#rArrcolor(green)(y=7#

Substitute the value of #y# to the first equation

#rarr-2x+5(7)=-3#

#rarr-2x+35=-3#

#rarr-2x=-3-35#

#rarr-2x=-38#

#rArrcolor(green)(x=(-38)/-2=38/2=19#

Check (Substitute the values of #x# and #y# to the first equation)

#color(orange)(-2(19)+5(7)=-3#

#color(orange)(-38+35=-3#

#color(orange)(-3=-3# =) correct!

Now to the second equation

#color(indigo)(19-3(7)=-2#

#color(indigo)(19-21=-2#

#color(indigo)(-2=-2# :) correct!

#:.# #x and y# have values of #19 and 7#