Respuesta :
The system of the equations have infinitely many solutions.
What is the solution of the equation?
The solution of the equation means the value of the unknown or variable.
The linear equation of two variable is given below.
6x + 3y = –12
6x + 3y + 12 = 0 ...1
–2x + 4 = y
2x + y – 4 = 0 …2
The standard equations are given as
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
Compare equation 1 and 2 with the standard equation. Then we have
a₁ = 6, b₁ = 3, c₁ = 12
a₂ = 2, b₂ = 1, c₂ = –4
If the ratio of the coefficient of x and y are different, then unique solution.
If the ratio of the coefficient of x and y are same, but constant term ratio is different, then no solution.
If the ratio of the coefficient of x and y and constant term is same, then infinitely many solutions.
a₁ / a₂ = 6/2 = 3
b₁ / b₂ = 3/1= 3
c₁ / c₂ = 12/(-4) = -3
Then the condition will be
a₁ / a₂ = b₁ / b₂ ≠ c₁ / c₂
The system of the equations have infinitely many solutions.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
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