Question

Consider that the system has infinitely many solutions. Which choice is the coefficient of y in the second equation? 5x + 10y = 15 x + __ y = 3

Answer 1

ANSWER

The coefficient of y is
$2$

EXPLANATION


The first equation is
$5x + 10y = 15$
We can rewrite this equation in the slope intercept form to get,


$10y = - 5x + 15$

We divide through by 10 to get,


$y = - \frac{1}{2} x + \frac{3}{2}$

The slope of this line is
$- \frac{1}{2}$

and the y intercept is
$\frac{3}{2}$


Let
$a$
be the coefficient of y in the second equation.

Then, we have

$x + ay = 3$


We rewrite this equation too in slope intercept form to get,

$ay = - x + 3$

Dividing through by
$a$

gives,

$y = - \frac{1}{a} x + \frac{3}{a}$


For the two equations to have infinitely many solution, then they must have the same slope and y intercept.


This means, that,


$- \frac{1}{a} = - \frac{1}{2}$

This implies that

$a = 2$

Therefore the coefficient of y must be 2.