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

Respuesta :

The statement that is true about the two given equations is that;

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

Equation of a line

The correct equations are given as;

–3x + 4y = 12    ----(eq 1)

¹/₄x – ¹/₃y = 1   -----(eq 2)

If we divide eq 1 by 12, we will arrive at;

-¹/₄x + ¹/₃y = 12

If we write it in slope intercept form and compare to eq 2, we will discover that they both have the same slope of ³/₄ and as such we can say they are parallel lines.

Since they are parallel lines, then they would not have any solution.

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