Question

how many solutions does the system of equations below have?
6x + 10y = 3
9x + 15y = -10
no solution
one solution
infinitely many solutions

Explanation:

Step1: Simplify first equation

Divide $6x + 10y = 3$ by 2:
$\frac{6x}{2} + \frac{10y}{2} = \frac{3}{2}$
$3x + 5y = \frac{3}{2}$

Step2: Simplify second equation

Divide $9x + 15y = -10$ by 3:
$\frac{9x}{3} + \frac{15y}{3} = \frac{-10}{3}$
$3x + 5y = -\frac{10}{3}$

Step3: Compare the two equations

Left sides are identical, right sides $\frac{3}{2}
eq -\frac{10}{3}$. This means parallel, non-overlapping lines with no intersection.

Answer:

no solution