How do solve the following linear system?: # 5x+y=6 , 12x-2y=-16 #?

3 Answers
May 12, 2018

Answer:

The solution to the linear system is #(-2/11,76/11)#.

The approximate solution is #(-0.18,6.9)#.

Explanation:

Solve the linear system:

#"Equation 1":# #5x+y=6#

#"Equation 2":# #12x-2y=-16#

We can solve the system by elimination.

Multiply Equation 1 by #2#.

#2(5x+y=6)#

#10x+2y=12#

Add Equation 1 and Equation 2.

#10x+2y=color(white)(....)12#
#12x-2y=-16#
#-------#
#22xcolor(white)(........)=-4#

Divide both sides by #22#.

#x=-4/22#

Simplify.

#x=-2/11# or #~~-0.18#

Substitute the value for #x# into Equation 1. Solve for #y#.

#5x+y=6#

#5(-2/11)+y=6#

Expand.

#-10/11+y=6#

Add #10/11# to both sides.

#y=6+10/11#

Multiply #6# by #11/11# to get an equivalent fraction with #11# as the denominator.

#y=6xx11/11+10/11#

#y=66/11+10/11#

#y=76/11# or #~~6.9#

The solution to the linear system is #(-2/11,76/11)#.

The approximate solution is #(-0.18,6.9)#.

graph{(5x+y-6)(12x-2y+16)=0 [-7.52, 6.53, 1.603, 8.627]}

May 12, 2018

Answer:

#x=-2/11#
#y=76/11#

Explanation:

Given -

#5x+y=6# --------- (1)
#12x-2y=-16# ------(2)

#5x+y=6# --------- (1) #xx 2#
#12x-2y=-16# ------(2)

#10x+2y=12#--------(3)
#12x-2y=-16# -------(2) -- #(3)+(2)#
#22x=-4#
#x=-4/22=-2/11#

#x=-2/11#

Plug in #x=-2/11# in equation (1)

#5(-2/11)+y=6#
#-10/11+y=6#

#y=6+10/11=(66+10)/11=76/11#

#y=76/11#

Answer:

#y=76/11 #

#x=-2/11#

Explanation:

Many ways, but my favorite is the elimination method, and fortunately, it works in this situation!

Let's make the equations look neater (put in #y=mx+b# form)

  • Equation 1: #" "5x+y=6 or y=-5x+6#
  • Equation 2: #" "12x-2y=-16 or y=6x+8#

The elimination method allows us to cancel out one of the variables, making it an easy algebra equation to solve for the remaining variable. You'll see.

Let's eliminate the #7# variable. In order to do that, we need to simply multiply one of the equations by negative one, let's do it to equation one.

  • Equation 1: #" "-y=+5x-6#
  • Equation 2: #" " y=6x+8#

Now, we add the equations together, getting one combined equation:

#0=11x+2#

#x=-2/11#

Now, we plug in the #x# value into one of the ORIGINAL equations to solve for #y#.

Equaiton 1:

#y=-5(-2/11)+6#

#y=76/11#