Nelly M.

asked • 12/12/14

What is the solution of the system of equations

6x-2y=4
-9x+3y=12

Ronald W.

Are you sure you wrote this right? Because in order to solve you must subtract o e equation from the other by getting either the x or y to cancel out.   6x-2y=4
       -9x+3y=12
 
You would multiply the first eq. by 3 to get 18x and the second eq. by 2 to get -18 so the x's would cancel, but when you multiply the 3into the first you get 18x-6y=12.  And when you multiply the second eq. by 2 you get -18x+6y=24. Now when you subtract these, both the x an the y go away, so you cant solve this.
 
18x-6x=12
-18x+6x=24
 
This equals:
 
0=36
 
So check to see if you copied right, this is unsolvable.
 
 
 
 
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12/12/14

1 Expert Answer

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Mark M. answered • 12/12/14

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The solution set to a system of equations is the set of points at which the graphs of those equations intersect.  For the system given in this problem, the two graphs never intersect, so the system has NO SOLUTION:
 
To see this, we can put each equation in slope-intercept form:
 
Solving 6x - 2y = 4 for y, we get y = 3x - 2 (a line with slope = 3 and
y-intercept = -2.  Solving -9x + 3y = 12 for y yields y = 3x + 4 (a line with slope = 3 and y - intercept = 4).  The lines are parallel so they never intersect which means that the system has no solution.  
 
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