Question

consider the system of equations.
-20x + 12y = 24
-5x + 3y = 6
how many (x, y) solutions does this system have?
choose 1 answer:
a no solutions
b exactly one solution
c infinitely many solutions
d none of the above

Explanation:

Step1: Simplify the first equation

Divide the equation $- 20x + 12y=24$ by $4$. We get $\frac{-20x + 12y}{4}=\frac{24}{4}$, which simplifies to $-5x + 3y = 6$.

Step2: Analyze the two - equations

The first simplified equation $-5x + 3y = 6$ is the same as the second given equation $-5x + 3y = 6$. This means the two equations represent the same line.

Answer:

C. Infinitely many solutions