SOLUTION: Hi much appreciated math tutors, I have a linear system problem that I'm not sure how to set up, it reads: Write a linear equation for the description below. Let x represent th

Question 971828: Hi much appreciated math tutors,
I have a linear system problem that I'm not sure how to set up, it reads:
Write a linear equation for the description below. Let x represent the number that is chosen and let y represent the final result.
Choose any number. Add 10 to the number. Multiply the result by 2. Subtract 18 from the result. Multiply the result by one half. Subtract the original number.
To find the number a person would have chosen to obtain a final result of 1, solve the linear system consisting of the equation you wrote and the equation y = 1. Explain your result. Thank you!
Found 2 solutions by rothauserc, ankor@dixie-net.com:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
y = [(2*(x+10) - 18) * (1/2)] - x
now we have y = 1 and we are asked to solve for x
1 = [(2*(x+10) - 18) * (1/2)] - x
1 = (2x + 20 - 18) * (1/2) - x
1 = x + 1 - x
1 = 1
therefore any number that is picked will yield a result of 1

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Choose any number.
Add 10 to the number.
Multiply the result by 2.
Subtract 18 from the result.
Multiply the result by one half. (dividing by two is the same)
Subtract the original number.
y = - x
:
To find the number a person would have chosen to obtain a final result of 1, solve the linear system consisting of the equation you wrote and the equation
:
y = - x
Multiply by 2,cancel the denominator and you have
2y = 2(x + 10) - 18 - 2x
2y = 2x + 20 - 18 - 2x
2y = 2x - 2x + 2
2y = 2
y = 1
:
You can see it is 1 no matter what x equals
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