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For what value of the constant a,

\(\begin{align*} 2x + 5y &= -8,\\ 6x &= 16 + a - 15y \end{align*}\)

does the system of equations below have infinitely many solutions?

 May 31, 2019
 #1
avatar+8842 
+3

2x + 5y  =  -8          Multiply both sides of this equation by  3.

6x + 15y  =  -24

 

6x  =  16 + a - 15y          Add  15y  to both sides of this equation.

6x + 15y  =  16 + a

 

So now our two equations are:

6x + 15y  =  -24

6x + 15y  =  16 + a

 

The system will have infinitely many solutions when both equations are identical.

So the system will have infinitely many solutions when....

 

-24  =  16 + a          Subtract  16  from both sides of this equation.

-40  =  a

a  =  -40

 

Check: https://www.desmos.com/calculator/r2kk6kmsgq

 May 31, 2019
 #2
avatar+7763 
+1

\(\begin{cases} 2x + 5y = -8\\ 6x + 15y = 16 + a \end{cases}\\ \begin{cases} 2x + 5y = -8\\ 2x + 5y = \dfrac{16 + a}3 \end{cases}\\ \dfrac{16+a}{3} = -8\\ 16 + a = -24\\ a = -40\)

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 Jun 1, 2019

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