How do you solve $x + y = 5$ $x + y = 5$ and $3x – y = –1$ using matrices?

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Answer 1 · 2018-07-16T16:32:16

$x=1 and y=4$

Here,

$x+y=5to(1)$ , $and$ $3x-y=-1to(2)$

Let us write in the matrix equation form :

$((1,1),(3,-1))((x),(y))=((5),(-1))$

We take ,

$A=((1,1),(3,-1))$ , $X=((x),(y))$ , $and B=((5),(-1))$

$:.AX=B$

Now, $detA=|(1,1),(3,-1)|=-1-3=-4!=0$

$:. "We can say that , " A^-1 " exists"$

Now , $adjA=((-1,-1),(-3,1))$

$:.A^-1=1/(detA)*adjA$

$:.A^-1=-1/4((-1,-1),(-3,1))$

We have,

$AX=B=>X=A^-1B$

$=>X=-1/4((-1,-1),(-3,1))((5),(-1))$

Using Product of two matrices :

$X=-1/4((-5+1),(-15-1))$

$=>X=-1/4((-4),(-16))$

$=>((x),(y))=((1),(4))$

$=>x=1 and y=4$

How do you solve x + y = 5 x+y=5x + y = 5 and 3x – y = –13x – y = –1 using matrices?