Question

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? 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 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 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 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

Answer:  The answer is (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

Step-by-step explanation:  Given the following system of equations:

$5x+2y=3,\\\\2x-3y=1.$

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. He multiplied equation 2 by 1.

The new system of equations will be

$(5x+2y)+(2x-3y)=3+1,\\\\1\times (2x-3y)=1\times 1,$

that is,

$7x-y=4,\\\\2x-3y=1.$

Thus, the correct option is (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.