Mathematics: Asystem 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 =

1/8 is the answer because it is less than 5/6....

Asystem of equations is shown below: x + 3y =

mckleinrivero

13.03.2022

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

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