How do you solve the linear system by substitution 3x + y =2 and -x -3y=6?

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Answer 1 · 2018-04-28T19:45:09

Like so:

#3x+y=2#

#-x-3y=6 => -6-3y=x#

Substitute this equation into the other system wherever you see #x#.

#3(-6-3y)+y=6#

Distribute #3# onto #(-6-3y)#

#-18-9y+y=2#

Combine alike terms

#-8y= 20#

Divide to solve for #y#

#(-8y)/-8=20/(-8) => y= -20/8#

Then solve for #x# using the value of #y#.

#-x-60/8 = 6#

#x=-108/8#

#y = -20/8#

Hope that helps!