Solve the following system of equations. (Write your answers as a comma-separated list. If there are infinitely many solutions, write a parametric solution using t and or s. If there is no solution, write NONE.) x_1+2x_2+6x_3=6 x_1+x_2+3x_3=3 (x_1,x_2,x_3)=?

Reggie 2021-02-09 Answered
Solve the following system of equations. (Write your answers as a comma-separated list. If there are infinitely many solutions, write a parametric solution using t and or s. If there is no solution, write NONE.)
x1+2x2+6x3=6
x1+x2+3x3=3
(x1,x2,x3)=?
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Expert Answer

Clara Reese
Answered 2021-02-10 Author has 120 answers

Step 1
Given to solve the system of equations.
The system of equations can be solved using elimination.
To eliminate x­3, the second equation is multiplied by 2 and subtracted from the first equation.

x1+2x2+6x3=6

x1+x2+3x3=3

(x1+2x2+6x3)2(x1+x2+3x3)=62(3)

x1+2x2+6x32x12x26x3=66x1=0

x1=0

Step 2

Plugging the value of x1 in the first and second equations:

It is seen that the equations after plugging the value of x1 are same. Hence, there are infinitely many solutions that satisfy the equation

x2+3x3=3

Hence, let x3=t.

So the value of x2 is given by:

Hence, the solution to the system of equations is given by

(x1,x2,x3)=(0,33t,t)

(0)+2x2+6x3=62x2+6x3=6x2+3x3=3 

(0)+x2+3x3=3x2+3x3=3

x2+3x3=3

x2+3(t)=3

x2+3t=3

x2=33t

Step 3

Result:

(x1,x2,x3)=(0,33t,t)

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Jeffrey Jordon
Answered 2021-11-08 Author has 2262 answers

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