Exercise 1 Page 485

We are asked to complete the given statement.

Notice that this is the first step in the method of elimination for solving systems of linear equations. Let's recall all the steps of this method.

1. Obtain coefficients for xy (or y) that differ only in sign by multiplying all terms of one or both equations by suitably chosen constants.
2. Add the equations to eliminate one variable, solve the resulting equation.
3. Back-substitute the value obtained in Step 2 into either of the original equations and solve for the other variable.
4. Check your solution in both of the original equations.

Now, we will perform the first step on the following system of linear equations. x+7y=3 & (I) - 2x+3y=1 & (II) Notice that all the coefficients are completely different. If we multiply Equation (I) by 2, the coefficients of the x-terms will differ only in signs.

Notice that the coefficients of x have opposite signs. Now the system is set up to be simplified. If we add Equation (I) to Equation (II), x-terms will cancel each other out. We successfully performed the first step of the elimination method! Now, let's complete the given statement.