Question

which statement is true about the equations -3x+4y=12 and 1 over 4 x - 1 over 3 y =1 A) The system of the equations has exactly one solution at (-8,3). B) The system of the equations has exactly one solution at (-4,3). C) The system of the equations has no solution; the two lines are parallel. D) The system of the equations has an infinite number of solutions represented by either equation.

Answer 1

Hi again :)

We need to solve -3x+4y=12 for x

Let's start by adding -4y to both sides

-3x+4y-4y=12-4y

-3x=-4y+12

x = (-4y+12)/-3

x= 4/3 y -4

Now substitute 4/3 y -4 for x in 1/4 x - 1/3 y =1

1/4 x -1/3 y =1

1/4 (4/3 y -4) -1/3 y =1

Use the distributive property

(1/4)(4/3 y) + (1/4)(-4) -1/3 y =1

1/3 y -1 - 1/3 y =1

Now combine like terms

(1/3y -1/3y) + (-1) =1

= -1

-1 = 1

Now add 1 to both sides

0=2

So there are no Solutions

The answer is C

I hope that's help Will :)

Answer 2

Answer:

C.The system of the equations has no solution; the two lines are parallel.

Step-by-step explanation: