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How do you solve the following system?: # 8x - 2y = - 4 , 2x - 3y = 5 #

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May 21, 2018

Answer:

See a solution process below:

Explanation:

Step 1) Solve each equation for #8x#:

  • Equation 1:

#8x - 2y = -4#

#8x - 2y + color(red)(2y) = -4 + color(red)(2y)#

#8x - 0 = -4 + 2y#

#8x = -4 + 2y#

  • Equation 2:

#2x - 3y = 5#

#color(red)(4)(2x - 3y) = color(red)(4) xx 5#

#(color(red)(4) xx 2x) - (color(red)(4) xx 3y) = 20#

#8x - 12y = 20#

#8x - 12y + color(red)(12y) = 20 + color(red)(12y)#

#8x - 0 = 20 + 12y#

#8x = 20 + 12y#

Step 2) Because the left side of both equations are the same we can equate the right side of both equations and solve for #y#:

#-4 + 2y = 20 + 12y#

#-4 - color(blue)(20) + 2y - color(red)(2y) = 20 - color(blue)(20) + 12y - color(red)(2y)#

#-24 + 0 = 0 + (12 - color(red)(2))y#

#-24= 10y#

#-24/color(red)(10)= (10y)/color(red)(10)#

#-12/5 = (color(red)(cancel(color(black)(10)))y)/cancel(color(red)(10))#

#-12/5 = y#

#y= -12/5#

Step 3) Substitute #-12/5# for #y# in either of the equations in Step 1 and calculate #x#:

#8x = -4 + 2y# becomes:

#8x = -4 + (2 xx -12/5)#

#8x = -4 + (-24/5)#

#8x = -4 - 24/5#

#8x = (5/5 xx -4) - 24/5#

#8x = -20/5 - 24/5#

#8x = -44/5#

#8x xx 1/8 = -44/5 xx 1/8#

#8/8x = -44/40#

#x = -11/10#

The Solution Is:

#x = -11/10# and #y= -12/5#

Or

#(-11/10, -12/5)#

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