How do you solve the following linear system: # -x + y = 3, 5x-2y=11 #?

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Answer 1 · 2018-06-14T16:33:50

See a solution process below:

Step 1) Solve the first equation for #y#:

#-x + y = 3#

#-x + color(red)(x) + y = 3 + color(red)(x)#

#0 + y = 3 + x#

#y = 3 + x#

Step 2) Substitute #(3 + x)# for #y# in the second equation and solve for #x#:

#5x - 2y = 11# becomes:

#5x - 2(3 + x) = 11#

#5x - (2 * 3) - (2 * x) = 11#

#5x - 6 - 2x = 11#

#5x - 6 + color(red)(6) - 2x = 11 + color(red)(6)#

#5x - 0 - 2x = 17#

#5x - 2x = 17#

#(5 - 2)x = 17#

#3x = 17#

#(3x)/color(red)(3) = 17/color(red)(3)#

#(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = 17/3#

#x = 17/3#

Step 3) Substitute #17/3# for #x# in the solution to the first equation at the end of Step 1 and calculate #y#:

#y = 3 + x# becomes:

#y = 3 + 17/3#

#y = (3/3 * 3) + 17/3#

#y = 9/3 + 17/3#

#y = 26/3#

The Solution Is:

#x = 17/3# and #y = 26/3#

Or

#(17/3, 26/3)#