## anonymous one year ago 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.

1. anonymous

@jim_thompson5910

2. LynFran

i did this same question today...

3. LynFran

choose the last option

4. LynFran

rewrite eq.1 y=1-2x sub it into eq.2 4x+2(1-2x)=-2 4x+2-4x=-2 2=-2

5. anonymous

Lemme try Cramer's Rule for this one.

6. LynFran

as u can see the x cancels so x can be any value, there will be an infinite # of solutions

7. anonymous

$\left[\begin{matrix}2 & 1 \\ 4 & 2\end{matrix}\right]\left[\begin{matrix}x \\ y\end{matrix}\right]=\left[\begin{matrix}1 \\ -2\end{matrix}\right]$ $AB=C$ $|A| = \left[\begin{matrix}2 & 1 \\ 4 & 2\end{matrix}\right] = (2\times2)-(1\times4)=0$

8. anonymous

This systems of equation doesn't work

9. anonymous

im sorry i still dont understand

10. anonymous

would the answer be 2=-2 @LynFran

11. anonymous

There is no x value, as there is no solution.

12. anonymous

That 2 lines are parallel

13. LynFran

its not x can carry an infinite # of solution

14. LynFran

@DecentNabeel check this out lol

15. anonymous

x cannot be 0 and -2 at the same time in systems of equation.

16. anonymous

So witch would it be ?

17. LynFran

check this out its explain in more detail http://openstudy.com/users/decentnabeel#/updates/55b9661ee4b0adef802b9b51

18. anonymous

If the determinant made from the coefficients equals zero, then there is not a single solution to the system.

19. LynFran

did u do that by substitution""

20. anonymous

Nah, I just put em in 2x2 matrix and get determinant

21. anonymous

If |A| = 0 , the system of equation doesn't work cause you can't divide by zero

22. 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.

23. anonymous

How can 2=-2

24. anonymous

The point is that 2 does not equal 2. There is no solution to the system of equations.