ANSWER
The coefficient of y is
[tex]2[/tex]
EXPLANATION
The first equation is
[tex]5x + 10y = 15[/tex]
We can rewrite this equation in the slope intercept form to get,
[tex]10y = - 5x + 15[/tex]
We divide through by 10 to get,
[tex]y = - \frac{1}{2} x + \frac{3}{2} [/tex]
The slope of this line is
[tex] - \frac{1}{2} [/tex]
and the y intercept is
[tex] \frac{3}{2} [/tex]
Let
[tex]a[/tex]
be the coefficient of y in the second equation.
Then, we have
[tex]x + ay = 3[/tex]
We rewrite this equation too in slope intercept form to get,
[tex]ay = - x + 3[/tex]
Dividing through by
[tex]a[/tex]
gives,
[tex]y = - \frac{1}{a} x + \frac{3}{a} [/tex]
For the two equations to have infinitely many solution, then they must have the same slope and y intercept.
This means, that,
[tex] - \frac{1}{a} = - \frac{1}{2} [/tex]
This implies that
[tex]a = 2[/tex]
Therefore the coefficient of y must be 2.
