Question

Which statement is true about the equations -3x + 4y = 12 and 1x - 3y = 1?

The system of the equations has exactly one solution at (-8, 3).
The system of the equations has exactly one solution at (-4, 3).
The system of the equations has no solution the two lines are parallel
The system of the equations has an infinite number of solutions represented by either equation

Answer 1

One solution: (-8,-3)

The system of the equations has exactly one solution at (-8, -3)

Explanation:

-3x + 4y = 12

x - 3y = 1

x = 1 + 3y

-3(1 + 3y) + 4y = 12

-3 - 9y + 4y = 12

-5y = 15

y = -3

x = 1 + 3(-3) = -8

One solution: (-8,-3)

Answer 2

one solution at (-8,-3)

Explanation:

-3x + 4y = 12

1x - 3y = 1

Multiply the second equation by 3

3(1x -3y ) = 1*3

3x -9y =3

Add this to the first equation

-3x+4y = 12

3x-9y =3

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

-5y = 15

Divide each side by -5

-5y/-5 = 15/-5

y =-3

Now solve for x

x -3y =1

x -3(-3) =1

x+9 =1

Subtract 9 from each side

x+9-9=1-9

x=-8

(-8,-3)