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Sagot :
In the elimination method, one variable is eliminated from the system of equations to find the value of the other.
To create the opposite terms of the x-variable-
- The first equation be multiplied by the number 4.
- Second equation be multiplied by the number -6.
What is the elimination method?
To solve the system of equations and find the value of the variables, the elimination method is used.
In this method, one variable is eliminated from the system of equations to find the value of the other.
Given information-
The system of the equation given in the problem is,
[tex]\rm 3x-\dfrac{1}{4}y=15[/tex]
The second equation given in the problem is;
[tex]\rm \dfrac{2}{3}x-\dfrac{1}{6}y=6[/tex]
To eliminate the x term, make the coefficient of x of both equations equal.
It can be done by multiplying the coefficient of x term of the first equation to the second equation and the coefficient of x term of the second equation to the first equation.
The first equation is multiplied by;
[tex]\rm 4\times 3x-4\times \dfrac{1}{4}y=15\times 4\\\\12x-y=50[/tex]
The second equation is multiplied by;
[tex]\rm -6 \times \dfrac{2}{3}x- -6 \times\dfrac{1}{6}y= -6 \times6\\\\-4x-y=-36\\\\4x+y=36[/tex]
Hence, to create the opposite terms of the x-variable-
The first equation is multiplied by the number 4.
The second equation is multiplied by the number -6.
Learn more about the elimination method here;
brainly.com/question/7013345
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