Question

Show that the system of equation on
-x-2y+2=0,1/2x-1/4y-1=0
has
a unique
solution​​

Answer 1

Answer:

Step-by-step explanation:

- x - 2y + 2 = 0

1/2x - 1/4y - 1 = 0 => 2x - y - 4 = 0  

The given equations are of form a₁x + b₁y + c₁ = 0 and a₂+b₂y+c₂ = 0

where a₁ = -1 , b₁ = -2, c₁ = 2; a₂ = 2, b₂ = -1, c₂ = -4

Now a₁/a₂ = -1/2 = -1/2 ; b₁/b₂ = -2/-1= 2

Since  a₁/a₂ ≠ b₁/b₂, therefore the system has unique solution.

Now to solve the equations:

- x - 2y + 2 = 0   ------------ [1]

2x - y - 4 = 0    ------------  [2]

multiply equation [1] by 2 and add to equation [2].

-2x - 4y + 4 = 0

2x - y  - 4 = 0

--------------------

  - 5y = 0

=> y = 0

Substitute value of y in equation [1]

-x - 0 + 2 = 0

=> -x + 2 = 0

=> x = 2.

Hence the x = 2, y = 0.

Answer 2

Answer:

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