Question

Which statement is true about the equations -3x + 4y = 12 and %x-Ay=17

O 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.
O The system of the equations has an infinite number of solutions represented by either equation.

Answer 1

Answer: b

Explanation:

Answer 2

No solution, the lines are parallel.

Explanation:

Any line can be represented by the equation

y = mx + b

where m is the slope and b is the y intercept.

-3x + 4y = 12

4y = 3x + 12

y = 3/4 x + 3

AND

1/4 x - 1/3 y = 1

- 1/3 y = - 1/4 x + 1

-4y = -3x + 12

4y = 3x - 12

y = 3/4 x - 3

If you get both equations in this form it is evident that the slopes m are the same (parallel) but the y intercept's b are different (not the same line). Therefore no solution.