How do solve the following linear system?: # 5x+y=6 , 12x-2y=-16 #?
3 Answers
The solution to the linear system is
The approximate solution is
Explanation:
Solve the linear system:
We can solve the system by elimination.
Multiply Equation 1 by
Add Equation 1 and Equation 2.
Divide both sides by
Simplify.
Substitute the value for
Expand.
Add
Multiply
The solution to the linear system is
The approximate solution is
graph{(5x+y-6)(12x-2y+16)=0 [-7.52, 6.53, 1.603, 8.627]}
#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
#5(-2/11)+y=6#
#-10/11+y=6#
#y=6+10/11=(66+10)/11=76/11#
#y=76/11#
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
- 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
- Equation 1:
#" "-y=+5x-6# - Equation 2:
#" " y=6x+8#
Now, we add the equations together, getting one combined equation:
Now, we plug in the
Equaiton 1: