How do you solve the system of equations #-5x + y = - 9# and #4x + 7y = 15#?

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Answer 1 · 2016-12-18T14:50:13

#x = 2# and #y = 1#

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

#-5x + color(red)(5x) + y = -9 + color(red)(5x)#

#0 + y = -9 + 5x#

#y = 5x - 9#

Step 2) Substitute #5x - 9# for #y# in the second equation and solve for #x#:

#4x + 7(5x - 9) = 15#

#4x + 35x - 63 = 15#

#39x - 63 = 15#

#39x - 63 color(red)( + 63) = 15 color(red)( + 63)#

#39x - 0 = 78#

#39x = 78#

#(39x)/color(red)(39) = 78/color(red)(39)#

#x = 2#

Step 3) Substitute #2# for #x# in the solution to the first equation in Step 1) and calculate #y#:

#y = (5*2) - 9#

#y = 10 - 9#

#y = 1#