Question

(05.02) A system of equations is shown below: 5x + 2y = 3 (equation 1) 2x − 3y = 1 (equation 2) A student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. If equation 2 is multiplied by 1, which of the following steps should the student use for the proof? (4 points) Select one: a. Show that the solution to the system of equations 7x − y = 4 and 2x − 3y = 1 is the same as the solution to the given system of equations b. Show that the solution to the system of equations 2x + 5y = 3 and 3x − 2y = 1 is the same as the solution to the given system of equations c. Show that the solution to the system of equations 9x + 4y = 5 and 7x − y = 4 is the same as the solution to the given system of equations d. Show that the solution to the system of equations −4x + 9y = 5 and 2x − 3y = 1 is the same as the solution to the given system of equations

Answer 1

A. Show that the solution to the system of equations 7x - y = 4 and 2x - 3y = 1 is the same as the solution to the given system of equations.

Answer 2

You are apparently being asked to identify the equations that result when

... 2x - 3y = 1

remains unchanged, and the first equation is replaced by

... (5x +2y) +(2x -3y) = (3) +(1).

The sum will be

... x(5+2) + y(2-3) = 3+1

... 7x - y = 4

So, the two equation in the system will now be

... 7x - y = 4

... 2x - 3y = 1

This description of the system corresponds to choice ...

... a. Show that the solution to the system of equations 7x - y = 4 and 2x - 3y = 1 is the same as the solution to the given system of equations.