How do you solve the system of equations #3a - 4b = 17# and #a + 2b = 1#?

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Answer 1 · 2016-12-09T13:40:06

#a = 3.8# and #b = -1.4#

Step 1) Solve the second equation for #a#:

#a + 2b - 2b = 1 - 2b#

#a + 0 = 1 - 2b#

#a = 1 - 2b#

Step 2) Substitute #1 - 2b# for #a# in the first equation and solve for #b#:

#3(1 - 2b) - 4b = 17#

#3 - 6b - 4b = 17#

#3 - 10b = 17#

#3 - 3 - 10b = 17 - 3#

#0 - 10b = 14#

#-10b = 14#

#(-10b)/(-10) = 14/(-10)#

#(cancel(-10)b)/(cancel(-10)) = -1.4#

#b = -1.4#

Step 3) Substitute #-1.4# for #b# into the solution for the second equation in Step 1) and calculate #a#:

#a = 1 - (2*-1.4)#

#a = 1 - (-2.8)#

#a = 1 + 2.8#

#a = 3.8#