Question

Without solving the systems, explain why the following systems must have the same solution.

Answer 1

Answer:

Both system of equations are intersecting

Step-by-step explanation:

The equations are of the form

ax+by+c=0

Two equations have no solution when

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

i) 4x−5y-13=0

3x+6y-11=0

$\frac{4}{3}\neq \frac{5}{6}\neq \frac{13}{11}$

So, they are intersecting lines and do have the same solution.

ii) 8x−10y-26=0

x−11y-2=0

$\frac{8}{1}\neq \frac{-10}{-11}\neq \frac{13}{11}$

So, they are intersecting lines and do have the same solution.