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?

Suppose that Yumiko has the linear system

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

Then, if she want to eliminate the variable y, she should multiply the equation (2) by 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 because when performing the multiplication, the coefficient that accompanies the y become 3.

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