# 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: