First Let we solve the Original system of equations:
equation (1): [tex] x+3y=5 [/tex]
equation (2): [tex] 7x-8y=6 [/tex]
Multiplying equation (1) by 7, we get
[tex] 7x+21y=35 -->(3) [/tex]
[tex] 7x-8y=6 --> (2) [/tex]
Subtracting,
[tex] 29y=29 [/tex] implies [tex] y=1 [/tex]
Then[tex] x=5-3(1)=2 [/tex]
Thus the solution of the original equation is[tex] x=2, y=1. [/tex]
Now Let we form the new equation:
Equation 2 is kept unchanged:
Equation (2):[tex] 7x-8y=6 [/tex]
Equation 1 is replaced with the sum of equation 1 and a multiple of equation 2:
Equation (1): [tex] 8x-5y=11 [/tex]
Now solve this two equations: [tex] 8x-5y=11,
7x-8y=6 [/tex]
Multiply (1) by 7 and (2) by 8,
[tex] 56x-35y=77 [/tex]
[tex] 56x-64y=48 [/tex]
Subtracting,[tex] 29y=29 [/tex] implies [tex] y=1 [/tex]
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
Answer:
8x − 5y = 11 and 7x − 8y = 6
Step-by-step explanation:
I took the test and got it right.
