anonymous
  • anonymous
Solve the system of equations by substitution. What is the solution for x? 2x + y = 1 4x + 2y = -2 x = 0 x = 2 There is no x value, as there is no solution. x can be any value, as there is an infinite number of solutions.
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
LynFran
  • LynFran
i did this same question today...
LynFran
  • LynFran
choose the last option

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LynFran
  • LynFran
rewrite eq.1 y=1-2x sub it into eq.2 4x+2(1-2x)=-2 4x+2-4x=-2 2=-2
anonymous
  • anonymous
Lemme try Cramer's Rule for this one.
LynFran
  • LynFran
as u can see the x cancels so x can be any value, there will be an infinite # of solutions
anonymous
  • anonymous
\[\left[\begin{matrix}2 & 1 \\ 4 & 2\end{matrix}\right]\left[\begin{matrix}x \\ y\end{matrix}\right]=\left[\begin{matrix}1 \\ -2\end{matrix}\right]\] \[AB=C\] \[|A| = \left[\begin{matrix}2 & 1 \\ 4 & 2\end{matrix}\right] = (2\times2)-(1\times4)=0\]
anonymous
  • anonymous
This systems of equation doesn't work
anonymous
  • anonymous
im sorry i still dont understand
anonymous
  • anonymous
would the answer be 2=-2 @LynFran
anonymous
  • anonymous
There is no x value, as there is no solution.
anonymous
  • anonymous
That 2 lines are parallel
LynFran
  • LynFran
its not x can carry an infinite # of solution
LynFran
  • LynFran
@DecentNabeel check this out lol
anonymous
  • anonymous
x cannot be 0 and -2 at the same time in systems of equation.
anonymous
  • anonymous
So witch would it be ?
LynFran
  • LynFran
anonymous
  • anonymous
If the determinant made from the coefficients equals zero, then there is not a single solution to the system.
LynFran
  • LynFran
did u do that by substitution""
anonymous
  • anonymous
Nah, I just put em in 2x2 matrix and get determinant
anonymous
  • anonymous
If |A| = 0 , the system of equation doesn't work cause you can't divide by zero
anonymous
  • anonymous
The original system of equations: 2x + y = 1 4x + 2y = -2 Modify the first equation: y = 1 - 2x Insert that into the second equation, then solve: 4x + 2(1 - 2x) = -2 4x + 2 - 4x = -2 4x - 4x + 2 = -2 2 = -2 The system of equations has no solution.
anonymous
  • anonymous
How can 2=-2
anonymous
  • anonymous
The point is that 2 does not equal 2. There is no solution to the system of equations.

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