SOLUTION: Trying to find a simple method of sovling the below linear equations for now and in the future. I thought I had it , when I set one variable to zero and solved for the remaining

Algebra.Com
Question 891212: Trying to find a simple method of sovling the below linear equations for now and in the future.
I thought I had it , when I set one variable to zero and solved for the remaining variable, then reversed the process. finally replacing the variable with the solutions. left me with mixed solutions.
Need help solving the linear system of equations:

2.
2x-6y=7, 5x+2y=10
A. Unique solution
(8,3)
B. Unique solution
(37/17, -15/34),
C. Infinite many solutions
t,6t+1)
D. No solution

3.
x-16y=9, 1/4x +4y= 8
A. Unique solution
(9,4)
B. Unique solution
(2, -4)
C. Infinite many solutions
t,8t+9)
D. No solution

4.
3x - 2y=7, 9x 6y = 14
A. Unique solution
(6,-4)
B. Unique solution
(8, 5),
C. Infinite many solutions
t,8t+5)
D. No solution

Thanks
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
You are not justified in setting a variable equal to zero. You might do that if you are looking for axis intercepts for one linear equation. You are not interested in such a solution for solving simultaneous linear equations.

Number 2 as an example:
2x-6y=7, 5x+2y=10.

These will intersect since slopes are 1/3 and -5/2. Not equal slopes, and not negative reciprocals.

Substitution Method,

;





.
-




------------(Alerted to mistake: now fixed; a digit "7" was missing)

-
Solution is and .


--
Possibly I made a mistake in one part of the solution. Look through my steps and maybe you will find the (possible ) mistake.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Trying to find a simple method of sovling the below linear equations for now and in the future.
I thought I had it , when I set one variable to zero and solved for the remaining variable, then reversed the process. finally replacing the variable with the solutions. left me with mixed solutions.
Need help solving the linear system of equations:

2.
2x-6y=7, 5x+2y=10
A. Unique solution
(8,3)
B. Unique solution
(37/17, -15/34),
C. Infinite many solutions
t,6t+1)
D. No solution

3.
x-16y=9, 1/4x +4y= 8
A. Unique solution
(9,4)
B. Unique solution
(2, -4)
C. Infinite many solutions
t,8t+9)
D. No solution

4.
3x - 2y=7, 9x 6y = 14
A. Unique solution
(6,-4)
B. Unique solution
(8, 5),
C. Infinite many solutions
t,8t+5)
D. No solution

Thanks






17x = 37 ------ Adding eqs (iii) & (i)





 ----- Substituting  for x in eq (i)















 ----- Reducing fraction to its lowest term 

RELATED QUESTIONS


Greetings mathematic overlords,

My conundrum is as follows, I have this equation I am... (answered by scott8148)

Hey, I have been trying for a while now and I can't seem  figure this one out. I would... (answered by stanbon)

Hi! 
I have been trying to use old, retired ACT exams to prepare to take the actual... (answered by josgarithmetic,MathLover1,MathTherapy)

I am trying to solve the following system of linear equation. 

x/4 - y/11 = -9/44... (answered by jim_thompson5910)

I am trying to determine the value of "x" from the following problem:

"This linear... (answered by josmiceli,greenestamps)

Could someone please tell me a "real life" situation where a straight line graph might be  (answered by stanbon)

I need the values of theta in which y = sec(theta) and I need the answer in radians. I... (answered by Alan3354)

two sums of y=x
            y=-3x-8
I know on a linear graph they meet at co-ordinates... (answered by nilan)

State whether the equations represent a linear, quadratic, or exponential function

1)... (answered by jsmallt9,lwsshak3)