How do you solve 9x + 2y = 5 and y - 2x + 3 = 0?

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Answer 1 · 2016-12-23T00:44:09

#x = 11/13# and #y = -17/13#

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

#y - 2x + 3 + color(red)(2x - 3) = 0 + color(red)(2x - 3)#

#y - 2x + color(red)(2x) + 3 - color(red)(3) = 0 + 2x - 3#

#y - 0 + 0 = 2x - 3#

#y = 2x - 3#

Step 2) Substitute #2x - 3# for #y# in the first equation and solve for #x#:

#9x + 2(color(red)(2x - 3)) = 5#

#9x + 4x - 6 = 5#

#(9 + 4)x - 6 = 5#

#13x - 6 = 5#

#13x - 6 + color(red)(6) = 5 + color(red)(6)#

#13x - 0 = 11#

#13x = 11#

#(13x)/color(red)(13) = 11/color(red)(13)#

#(color(red)(cancel(color(black)(13)))x)/color(red)(cancel(color(black)(13))) = 11/13#

#x = 11/13#

Step 3) Substitute #11/13# for #x# in the solution to the second equation in Step 1) and calculate #y#:

#y = 2(color(red)(11/13)) - 3#

#y = 22/13 - 3#

#y = 22/13 - (3 * 13/13)#

#y = 22/13 - 39/13#

#y = -17/13#