Question

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

Answer 1

The correct option is (B). $3x+5y=29$ And $-3x-12y=-48$.

Given Equations,

$3x + 5y = 29......(1)$

$x + 4y = 16.......(2)$

We have to find out  Which system of equations is equivalent to the Given system of Equations.

 1). System of equation are,

$3x+5y=29\\-x-4y=16$

taking - common and transposing to R.H.S we get,

$x+4y=-16$

This equation is not equal to equal (2), so the option (1) is not the system of equation equivalent to given Equations.

Similarly, on checking other options,

2. system of equation,

$3x+5y=29\\-3x-12y=-48$

Taking -3 common from L.H.S. we get,

$-3(x+4y)=-48\\\\x+4y=\dfrac{-48}{-3}$

$x+4y=16$.

Hence the Above system of equation is equivalent to the given system of equation.

So, there is no need to check option (3) and option (4).

Hence the correct option is (B).

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