Question

Determine if the given set of equations has 1 solution, no solution or infinitely many solutions. Include your reasoning for your answer.

3x−4y=8
4y−4x=6

Answer 1

Answer:

1 solution It is (-14, -12.5).

Step-by-step explanation:

3x−4y=8

4y−4x=6

Adding the 2 equations eliminates the 4y:

3x - 4x = 14

x = -14

So

-42 - 4y = 8

4y = -50

y = -12.5,

Answer 2

Answer:

one solution

Step-by-step explanation:

3x - 4y = 8             a₁ = 3  and  b₁ = -4

-4x + 4y = 6          a₂ = -4  and b₂ = 4

Set of equations has on solution if

$\dfrac{a_{1}}{a_{2}} \neq \dfrac{b_{1}}{b_{2}}\\\\\\\dfrac{3}{-4} \neq \dfrac{-4}{4}$