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As a first step in solving the system shown, Yumiko multiplies both sides of the equation 2x – 3y = 12 by 6. By what factor should she multiply both sides of the other equation so that she can add the equations and eliminate a variable?

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Answer:

Suppose that Yumiko has the linear system

[tex]2x-3y=12 \;;(1)\\ax+by=c \;; (2)[/tex]

Since she multiplies the first equation by 6 then she obtains the equation

[tex]12x-18y=72[/tex]

Then, if she want to eliminate the variable y, she should multiply the equation (2) by [tex]\frac{-12}{a}[/tex] because when performing the multiplication, the coefficient that accompanies the x become 12.

If she want to eliminate the variable y, she should multiply the equation (2) by [tex]\frac{3}{b}[/tex] because when performing the multiplication, the coefficient that accompanies the y become 3.

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