Answer:
Yumiko should multiply the other equation by 3.
If she adds the two equations she would be left with the variable 'x'.
Step-by-step explanation:
Given the two equations are as follows:
[tex]$ 2x - 3y = 12 \hspace{5mm} \hdots (1) $[/tex]
[tex]$ 5x + 6y = 18 \hspace{5mm} \hdots (2) $[/tex]
It is given that she multiplies the first equation by 6. Therefore, (1) becomes
[tex]$ 12x - 18y = 72 \hspace{15mm} \hdots (a) $[/tex]
Now, note that the sign of the variable 'y' is negative. So, if we make the co-effecient of 'y' equal in both the cases, add them it would result in the elimination of the variable 'y'.
The co-effecient of y in Equation (2) is 6. To make it 18 like it is in Equation (1), we multiply throughout by 3.
Therefore, Equation (2) becomes:
[tex]$ 15x + 18y = 54 \hspace{5mm} \hdots (b) $[/tex]
Now, we add Equation (a) and Equation (b).
[tex]$ \implies 12x - 18y + 15x + 18y = 72 + 54 $[/tex]
[tex]$ \implies 27x = 126 $[/tex]
Factor: 3
Equation: 27x = 126
