How do you solve the system of equations #\frac { 3} { 4} x + \frac { 1} { 2} y = - \frac { 3} { 4}# and #\frac { 2} { 3} x + \frac { 2} { 3} y = \frac { 2} { 3}#?

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Answer 1 · 2016-11-14T04:49:02

Solve equation 1 for y (I think that would be easiest).

#1/2y = -3/4 - 3/4x#

#y = (-3/4)/(1/2) - (3/4)/(1/2)x#

#y = -3/2 - 3/2x#

#:.2/3x + 2/3(-3/2 - 3/2x) = 2/3#

#2/3x - 1 - x = 2/3#

#-1/3x = 5/3#

#x = (5/3)/(-1/3)#

#x = -5#

#2/3x + 2/3y = 2/3#

#2/3(-5) + 2/3y = 2/3#

#2/3y = 2/3 + 10/3#

#2/3y = 4#

#y= 4/(2/3)#

#y = 6#

The solution set is #{-5, 6}#.

Hopefully this helps!