Question

A system of equations is shown below:

x + 3y = 5 (equation 1)
7x – 8y = 6 (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 3x + y = 5 and 8x –7y = 6 is the same as the solution to the given system of equations

Answer 1

Show that the solution to the system of equations 3x + y = 5 and 8x –7y = 6 is the same as the solution to the given system of equations
Show that the solution to the system of equations 8x – 5y = 11 and 7x – 8y = 6 is the same as the solution to the given system of equations
Show that the solution to the system of equations 15x + 13y = 17 and 7x – 8y = 6 is the same as the solution to the given system of equations
Show that the solution to the system of equations –13x + 15y = 17 and 7x – 8y = 6 is the same as the solution to the given system of equations

Answer 2

@triciaal

Answer 3

to solve the first part
multiply equation 1 by 8 and equation 2 by 3

if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2,

can you verify this?

Answer 4

says equation 2 unchanged and equation 2 with a multiple

Answer 5

to solve by elimination the objective is to make the coefficient of one variable equal and opposite so they will cancel out when the equations are added. this will give one equation with one unknown. solve for this variable. use this value in either of the original to find the value of the other variable. It is a good practice to check your solution in the original equation because it is extremely easy and common to make arithmetic errors.