Which system of equations is equivalent to the following system? 3x + 5y = 29 x + 4y = 16 3x + 5y = 29 −x − 4y = 16 3x + 5y = 29 −3x − 12y = −48 −3x − 5y = 29 x + 4y = 16 −9x − 15y = 87 x + 4y = 16

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Answer:

Option 3x+5y=29 and -3x-12y=-48 is the system of equations equivalent to the given system of equations 3x+5y=29 and x+4y=16

Step-by-step explanation:

Given system of equations  is 3x+5y=29 and x+4y=16

To find the equivalent system of equations to the given system of equations :

Option 3x+5y=29 and -3x-12y=-48 is the system of equations represents the given system of equations.

Because we can write the given equations as below

3x+5y=29 and x+4y=16

x+4y=16 rewritting as below

When multiply the above equation into (-3) we get

[tex](-3)\times (x+4y)=16\times (-3)[/tex]

[tex]-3x-4y=-48[/tex] as same as the equation x+4y=16 so we can say that they are equivalent

Therefore Option 3x+5y=29 and -3x-12y=-48 is the system of equations represents the given system of equations

Therefore 3x+5y=29 and -3x-12y=-48 is the system of equations equivalent to the given system of equations 3x+5y=29 and x+4y=16

[tex]3x + 5y = 29 \ and \ -3x -12y = -48[/tex],  is the system of equations equivalent to the given system of equations [tex]3x+5y=29[/tex] [tex]and[/tex]  [tex]x+4y=16[/tex].

Given that,

Equation;  3x + 5y = 29, x + 4y = 16

We have to determine,

Which system of equations is equivalent to the following system.

According to the question,

System of equations;

[tex]3x + 5y = 29,\\x + 4y = 16[/tex]

To find the equivalent system of equation is equivalent to the system check all the options given below.

1). System of equation are;

   [tex]3x + 5y = 29,\\ -x - 4y = 16[/tex]

Multiply by (-) in the equation,

[tex]-x-4y = 16\\x +4y = -16[/tex]

Therefore the equation is not equivalent to [tex]3x + 5y = 29,\ x + 4y = 16[/tex].

2). System of equation is;

    [tex]3x + 5y = 29\\-3x - 12y = -48[/tex]

Taking common factor -3 from equation 2,

[tex]-3x -12y = -48\\\\-3( x+4 ) = -48[/tex]

Divided by -3 on both the sides,

[tex]-3( x+4 ) = -48\\\\\dfrac{-3}{-3}(x+4) = \dfrac{-48}{-3}\\\\x + 4 = 16[/tex]

Hence. The required system of equations is equivalent to the,[tex]3x + 5y = 29 , \ -3x - 12y = -48[/tex]

   

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