Question

-6x + 4y = 2;
3x – 2y = 4
Consider the system of equations above. If (x, y) is a solution of the equations above, then how many possible values are there for (x, y) ?

• A. No Solution
• B. One solution
• C. Two solutions
• D. Infinitely many solutions

Answer 1

The correct option is A No Solution

Ratio of coefficients of $x=-\frac{6}{3}=-2$
Ratio of coefficients of $y=-\frac{4}{-2}=-2$
Ratio of constant terms $=\frac{2}{4}=\frac{1}{2}$
This describes a situation involving parallel lines when the above equations are visualised graphically.
Therefore, the system of equations has no solutions.