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Question 1165621: Solve the system:
{4x1+x2=7
{12x1+3x2=21
[x1]=[]+s[]
[x2]=[]+s[]
Answer by ikleyn(52747) (Show Source):
You can put this solution on YOUR website! .
Solve the system:
{4x1+x2=7
{12x1+3x2=21
[x1]=[]+s[]
[x2]=[]+s[]
~~~~~~~~~~~~~~~~~~~~~~~
In this assignment, the second equation is 3 times first equation.
So, actually, two equations of the given system are equivalent to one equation
4x + y = 7.
The solution for this equation is
y = 7 - 4x.
It means that 'x' is a "free variable", which may have any value;
then the corresponding 'y' value is calculated as 7 - 4x.
In parametric form, we put
x = s,
y = 7 - 4s.
Thus we get the parametric solution to the given system of equations
in the form, which is requested in the assignment.
At this point, the problem is solved completely, with comprehensive explanations.
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