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 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 1

Answer:

8x − 5y = 11 and 7x − 8y = 6

Step-by-step explanation:

I took the test and got it right.

Answer 2

First Let we solve the Original system of equations:

equation (1): $x+3y=5$

equation (2): $7x-8y=6$

Multiplying equation (1) by 7, we get

$7x+21y=35 -->(3)$

$7x-8y=6 --> (2)$

Subtracting,

$29y=29$ implies $y=1$

Then$x=5-3(1)=2$

Thus the solution of the original equation is$x=2, y=1.$

Now Let we form the new equation:

Equation 2 is kept unchanged:

Equation (2):$7x-8y=6$

Equation 1 is replaced with the sum of equation 1 and a multiple of equation 2:

Equation (1): $8x-5y=11$

Now solve this two equations: $8x-5y=11, \\ 7x-8y=6$

Multiply (1) by 7 and (2) by 8,

$56x-35y=77$

$56x-64y=48$

Subtracting,$29y=29$ implies $y=1$

Then x=2.

so the solution for the new system of equation is x=2, y=1.

This 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