Question

The graph for the following system of equations :

$2x+3y=5and6x+9y=40$ is shown

S1: $\frac{a_1}{a_2}$= $\frac{b_1}{b_2}$ ≠ $\frac{c_1}{c_2}$

S2 : The two lines intersect each other.

• A. S1 is true but S2 is false
• B. S1 is false but S2 is true
• C. S1 and S2 are true
• D. S1 and S2 are false

Answer 1

The correct option is A

S1 is true but S2 is false

For a pair of equations, $a_1$x + $b_1$y + $c_1$= 0 and $a_2$x +$b_2$y +$c_2$ = 0 , if $\frac{a_1}{a_2}$ = $\frac{b_1}{b_2}$ ≠ $\frac{c_1}{c_2}$ , then the lines are parallel.

For the given equations

$2x+3y=5and6x+9y=40$

$\frac{2}{6}$ = $\frac{3}{9}$ ≠ $\frac{5}{40}$

Hence the lines are parallel and do not intersect each other.