Question

Consider the system of equations.

Equation (1) x + y = 7
Equation (2) 3x – 2y = 1

Part A) Show that (3, 4) is a solution of this system.




Part B) Construct a new equation (3) by adding 5 times equation (1) to equation (2).

Multiply equation (1) by 5 and write it here →

Equation (2) +
_________________
Equation (3)


Part C) Show that (3, 4) is a solution of the system consisting of equations (1) and (3).


Part D) Explain why the system of equations (1) and (2) and the system of equations (1) and (3) have the same solution.

Answer 1

Answer:A: (3,4)

B:Equation (3) 8x+3y=36

C:(3,4)

D. Because both of systems have equation (1) , Equation (3) is combination of (1) and (2), so equation (1) is common for both systems.

Explanation:

A. x+y=7

3x-2y=1

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y=7-x

3x-2*(7-x)=1

3x-14+2x=1

5x=1+14

x=15/5

x=3

y=7-3=4

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B. 5x+5y=35

+ 3x-2y=1

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Equation (3) 8x+3y=36

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C. x+y=7

8x+3y=36

----------------------------

x=7-y

56-8y+3y=36

-5y=-20

y=4

x=7-4

x=3

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D. Because both of systems have equation (1) , Equation (3) is combination of (1) and (2), so equation (1) is common for both systems.