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
<pre>
{{{system (2x - 6y = 7_____eq (i), 5x + 2y = 10____eq (ii))}}}
{{{system (15x + 6y = 30___Multiplying_eq_(ii)_by_3_____eq_(iii), 2x - 6y = 7______eq (i))}}}
17x = 37 ------ Adding eqs (iii) & (i)
{{{highlight_green(x = 37/17)}}}

{{{2(37/17) - 6y = 7}}} ----- Substituting {{{37/17}}} for x in eq (i)
{{{74/17 - 6y = 7}}}
{{{74/17 - 6y = 119/17}}}
{{{- 6y = 119/17 - 74/17}}}
{{{- 6y = 45/17}}}
{{{y = (45/17)/- 6}}}
{{{y = (45/17) * (1/-6)}}}
{{{y = - 45/102}}}
{{{highlight_green(y = - 15/34)}}} ----- Reducing fraction to its lowest term