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For what value of the constant $a$ does the system of equations below have infinitely many solutions? \begin{align*} 2x + 5y &= -8,\\ 6x &= 16 + a - 15y \end{align*}

 Jul 24, 2021
 #1
avatar+34315 
+1

2x + 5y = -8

6x + 15y = a     Multiply top equation by 3 to get:

6x + 15y = -24                if a and -24 are equal the two equations are the same and there are infinite solutions 

 

a = -24

 Jul 24, 2021
 #2
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0
That is so wrong.
 Jul 25, 2021
 #3
avatar+114464 
+1

2x+5y=-8

multiply by 3

6x+15y=-24      (1)

 

6x=16+a-15y

6x+15y = 16+a     (2)

 

These will be the same line and therefore have infinite simultaneous solutions if

 

16+a = -24

a= -40

 Jul 26, 2021

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