Question

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

O The system of the equations has exactly one solution at (-8, 3).
O 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.
O The system of the equations has an infinite number of solutions represented by either equation.

Answer 1

None of these answers is true

Explanation:

1x - y = 1 ⇒ x - 1 = y

-3x + 4y = 12

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

-3x + 4x - 4 = 12

x - 4 = 12

x = 16 ⇒ 16 - 1 = y ⇒ y = 15

Therefore the system of the equations has exactly one solution at (16,15)

Answer 2

D- There are infinite solutions

Explanation:

-3x + 4y= 12 is the same as 1/4x -1/3y = 1.

1/4x multiplied by 12 is 3x

-1/3y multiplied by 12 is -4y

To flip the negatives you multiply by -1 to get -3x + 4y+ 12 on both equations