Question

$-6x+8y=2$ , $3x-4y=-3$
Consider the system of equations above. How many $(x,y)$ solutions does this system have?

• A. No solutions
• B. Exactly one solution
• C. Exactly two solutions
• D. Infinitely many solutions

Answer 1

The correct option is A No solutions

Lets see $-6x+8y=2$
$3x-4y=-3$
Ratio of $x$ coefficient $=\frac{-6}{3}=-2$
Ratio of $y$ coefficient $=\frac{8}{-4}=-2$
Ratio of constant $=\frac{2}{-3}$
So from here, we can see that ratio of $x$ coefficient = Ratio of $y$ coefficient $\ne$ Ratio of constant
Therefore, these two lines are paralled and there is no solution of the given system of equations.