How do you solve the following system: #3x + 8y = -2, -2x + 5y = 20#?

1 Answer
Oct 2, 2017

Answer:

See a solution process below:

Explanation:

Step 1: Solve each equation for #6x#:

  • Equation 1: #3x + 8y = -2#

#3x + 8y - color(red)(8y) = -2 - color(red)(8y)#

#3x + 0 = -2 - 8y#

#3x = -2 - 8y#

#color(red)(2) * 3x = color(red)(2)(-2 - 8y)#

#6x = (color(red)(2) * -2) - (color(red)(2) * 8y)#

#6x = -4 - 16y#

  • Equation 2: #-2x + 5y = 20#

#-2x + 5y - color(red)(5y) = 20 - color(red)(5y)#

#-2x + 0 = 20 - 5y#

#-2x = 20 - 5y#

#color(red)(-3) * -2x = color(red)(-3)(20 - 5y)#

#6x = (color(red)(-3) * 20) - (color(red)(-3) * 5y)#

#6x = -60 - (-15y)#

#6x = -60 + 15y#

Step 2: Now with the left side of both equations equal we can equate the right side of the equations and solve for #y#:

#-4 - 16y = -60 + 15y#

#color(blue)(60) - 4 - 16y + color(red)(16y) = color(blue)(60) - 60 + 15y + color(red)(16y)#

#56 - 0 = 0 + (15 + color(red)(16))y#

#56 = 31y#

#56/color(red)(31) = (31y)/color(red)(31)#

#56/31 = (color(red)(cancel(color(black)(31)))y)/cancel(color(red)(31))#

#56/31 = y#

#y = 56/31#

Step 3: Substitute #56/31# for #y# in the solution to either equation in Step 1 and solve for #x#:

#6x = -60 + 15y# becomes:

#6x = -60 + (15 * 56/31)#

#6x = (31/31 * -60) + 840/31#

#6x = -1860/31 + 840/31#

#6x = -1020/31#

#color(red)(1/6) * 6x = color(red)(1/6) * -1020/31#

#6/6x = -170/31#

#x = -170/31#

The Solution Is: #x = -170/31# and #y = 56/31# or #(-170/31, 56/31)#