Mathematics: 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

Consider that the system has infinitely many solutions.

Ответ:

lishalarrickougdzr

10.03.2022

Mathematics

ANSWER

The coefficient of y is

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

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

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