How do you solve the system $9 x + 3 y = 1, 5 x + y = 1$ $9x+3y=1, 5x+y=1$ using matrix equation?

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Answer 1 · 2016-12-08T16:36:28

The answer is $x = \frac{1}{3}$ $x=1/3$ and $y = - \frac{2}{3}$ $y=-2/3$

Let' write the matrix corresponding to the 2 equations

$((9,3),(5,1))*((x),(y))=((1),(1))$

Let $A=((9,3),(5,1))$

Then

$((x),(y))=A^(-1)*((1),(1))$

We must calculate the inverse of matrix $A$

The inverse of matrix $((a,b),(c,d))$ is

$1/(ad-bc)*((d,-b),(-c,a))$

So,

$A^(-1)=1/(-6)((1,-3),(-5,9))$

$=((-1/6,1/2),(5/6,-3/2))$

Verification

$A*A^(-1)=I$

$((-1/6,1/2),(5/6,-3/2))*((9,3),(5,1))=((1,0),(0,1))=I$

Now, we can solve our equation

$((x),(y))=((-1/6,1/2),(5/6,-3/2))*((1),(1))$

$x=-1/6+1/2=1/3$

$y=5/6-3/2=-2/3$

How do you solve the system 9x+3y=1, 5x+y=19x+3y=1,5x+y=19x+3y=1, 5x+y=1 using matrix equation?