Using augmented matrix

[frctl]

Solve using augmented matrix methods
x₁ - 2x₂ = 1
2x₁ - x₂ = 5

My work is the following:


When I check the back of the book, the answer is:
x₁ = 3, x₂ = 1

 

[Steven G]

Why are you checking the back of the book? Just check your answer.

1(-9) - 2(-5) = -9 + 10 = 1. Looking good.

2(-9) - 1(-5) = 18 + 5 = -13 \(\displaystyle \neq\)5.

So your answer is wrong.

You wrote -R₂ --> R₂ was not done correctly. After all -2*2 is not 0.

Please try again and post back

 

[frctl]

Now I obtain the answer

Checking my work though:
1(3) - 2(1) = 1
2(3) - 1(1) = 5

Is this correct?

 

[Steven G]

Now I obtain the answer
View attachment 17279
Checking my work though:
1(3) - 2(1) = 1
2(3) - 1(1) = 5

Is this correct?

Yes your work is correct. Good job.

 

[frctl]

I'm not sure. Is the requirement of my check to equal 1, if so then my work is incorrect and if this check (obtaining 5) is fine then my work is correct

 

[pka]

I'm not sure. Is the requirement of my check to equal 1, if so then my work is incorrect and if this check (obtaining 5) is fine then my work is correct

Look here

 

[Steven G]

I'm not sure. Is the requirement of my check to equal 1, if so then my work is incorrect and if this check (obtaining 5) is fine then my work is correct

You need to check both equations.
Remember that x₁-2x₂ =1 is the equation of a line. If you rename x₁ to y and x₂ to x you get y-2x=1 or y=2x+1. Now many many points are on this line. Similarly, many points are on the line 2y=x+5. In the work that you did you found where the points intersect at. That is why your solution must be verified in both equations.

Please note for example that if x₁= 5 and x₂= 2, then this point satisfies the 1st equation but not the 2nd equation.