Solve the system below by the method of your choice Identify

Solve the system below by the method of your choice. Identify systems with no solution and systems
with infinitely many solutions using set notation to express their solution sets.

12. solve the system bel with infinitely many sol 4-r 2y A. (5, -4) B. ((0, 6) C. 0

Solution

Given

y = 6 - 2x                      (1)

4x + 2y = 12                 (2)

rearranging equation (1)

adding both sides \"2x\"

2x + y = 6 - 2x + 2x

2x + y = 6                  (3)

we represent a line as => ax + by = c

here \"a\" is the coefficient of x.

\"b\" is the coefficient of y.

and \"c\" is the constant term.

a₁ / a₂ = b₁ / b₂ = c₁ / c₂

here a₁ , b₁ , c₁ are for the first line and a₂ , b₂ and c₂ are for the second line

2x + y = 6

4x + 2y = 12  

therefore

2/4 = 1/2 = 6/12

we get

1/2 = 1/2 = 1/2

since the ratio of coefficient of two lines are equal therefore these lines are Coincident line or they have many solutions.