Respuesta :
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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