Question

Select values to multiply each equation by to form opposite terms for the x-variable. One-third x + one-sixth y = 2 One-half x + three-fourths y = negative 3

Answer 1

Answer:

First equation: 1/2

Second equation: -1/3

Step-by-step explanation:

We get the following equations:

$\frac{1}{3}x+\frac{1}{6}y=2$          first equation

$\frac{1}{2}x+\frac{3}{4}y=-3$       2nd equation

Then, to obtain opposite terms for the x variable, we need to identify the coefficient of the x for the 1st equation and the 2nd equation as:

The coefficient for x in the 1st equation is $\frac{1}{3}$ and the coefficient for x in the 2nd equation is $\frac{1}{2}$

Finally, we need to multiply 1st equation with the coefficient of the 2nd equation and multiply the 2nd equation with the negative of the coefficient of the 1st equation.

We multiply by the negative of the coefficient of the 1st equation because we need to find opposite terms for x.

So, the first equation is equal to:

$(\frac{1}{3}x+\frac{1}{6}y)*\frac{1}{2} =2*\frac{1}{2} \\\frac{1}{6}x+\frac{1}{12}y=1$        

The second equation is:

$(\frac{1}{2}x+\frac{3}{4}y)*\frac{-1}{3} =-3*\frac{-1}{3} \\\frac{-1}{6}x+\frac{-1}{4}y=1$

Now, the coefficients for x, 1/6 and -1/6, are opposite terms.