How do you solve the following system: #3x + 4y = 11 , 7x+15y=32 #?

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Answer 1 · 2016-11-21T22:07:48

#y = 19/17# and #x = 37/17#

Step 1) Solve the first equation for #x#L

#3x + 4y - 4y = 11 - 4y#

#3x + 0 = 11 - 4y#

#3x = 11- 4y#

#(3x)/3 = (11 - 4y)/3#

#1x = (11 - 4y)/3#

#x = 11/3 - (4y)/3#

Step 2) Substitute #11/3 - (4y)/3# for #x# in the second equation and solve for #y#:

#7*(11/3 - (4y)/3) + 15y = 32#

#77/3 - (28y)/3 + 15y = 32#

#77/3 - 77/3 - (28y)/3 + (3/3)*15y = 32 - 77/3#

#(-28y)/3 + (45y)/3 = (3/3)*32 - 77/3#

#(17y)/3 = 96/3 - 77/3#

#(17y)/3 = 19/3#

#(3/17)(17y)/3 = (19/3)(3/17)#

#y = 19/17#

Step 3) Substitute #22/17# for #y# in the solution to the first equation to calculate #x#:

#x = 11/3 - (4/3)(19/17)#

#x = 11/3 - 76/51#

#x = (17/17)(11/3) - 76/51#

#x = 187/51 - 76/51#

#x = 111/51#

#x = (3/3)(37/17)#

#x = 37/17#