Question 218305
Can someone explain the Gauss-Jordan elimination method to solve this system of linear equations?


2x+ y= 5  Equation A
4x+ 3y= 11  Equation B


Is the solution (2,1) or am I wrong?  thank you.


Step 1  Check (2,1) by substituting into Equations A and B where x=2 and y=1.


2*2+1= 5  or 5=5 which satisfies Equation A.


4*2+3*1=8+3=11 of 11=11  which satisfies Equation B.


Step 2.  The elimination method in this example means when you multiply either Equation A or B by a factor such that when you add or subtract these two equations, one of the variables x or y will be eliminated.  When you eliminate a variable, then you have an equation with one variable in this case.


Step 3.  As an example, take Equation A and multiply by -2.  This yields


{{{-4x-2y=-10}}}  Equation A1
{{{4x+3y=11}}} Equation B


Now when you add these two equations A1 and B, this will yield


{{{-4x+4x-2y+3y=-10+11}}}


{{{y=1}}}  This leaves a single equation with y=1.


Step 4.  As another example take Equation A and multiply by -3.  This yields


{{{-6x-3y=-15}}} Equation A2
{{{4x+ 3y= 11}}}  Equation B


Adding these two Equations A2 and B yields


{{{-6x+4x-3y+3y=-15+11}}}


{{{-2x=-4}}}   where we eliminated the y-terms and have a single variable in the equation.


Now divide -2 to both sides of the equation


{{{x=2}}}


So the solution is x=2 and  y=1 or at point (2,1) as a solution given earlier in the problem.


I hope the above steps were helpful.


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And good luck in your studies!


Respectfully,
Dr J

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