How do you solve the system #2x - 15y = 33# and #-3x + 4y = - 5#?

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Answer 1 · 2015-06-28T01:58:53

#x = -171/111# and #y = -89/37#

(1) #2x-15y=33#
(2) #-3x+4y=-5#

Let's eliminate the #x# variable.

Multiply Equation (1) by 3 and Equation (2) by 2. This gives

(3) #6x-45y=99#
(4) #-6x+8y=-10#

Add Equations (3) and (4).

(5) #-37y = 89#

(6) #y = -89/37#

Substitute (6) in (2).

#-3x+4y= -3x + 4(-89/37) = -3x – 356/37 = -5#

#-3x = 356/37 -5 = (356-185)/37 = 171/37#

#x = -171/111#

Check: Substitute in (2).

#-3x +4y = -3(-171/111) +4(-89/37) = 513/111 -356/37 = (37×513-111× 356)/(111×37) = (18981-39516)/4107 = -20535/4107 = 5#