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`

Step-by-step 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 = - (1)/(2) x + (3)/(2)`

The slope of this line is

`- (1)/(2)`

and the y intercept is

`(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 = - (1)/(a) x + (3)/(a)`


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


This means, that,



`- (1)/(a) = - (1)/(2)`

This implies that


`a = 2`

Therefore the coefficient of y must be 2.