How do you solve $5 x + 3 y = - 4.5$ $5x + 3y = -4.5$ and $2 x + 1.2 y = - 1.8$ $2x + 1.2y = -1.8$ using matrices?

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Answer 1 · 2017-11-04T08:42:21

no solution, the lines are parallel .

$5 x + 3 y = - 4.5 - - (1)$ $5x+3y=-4.5--(1)$

$2 x + 1.2 y = - 1.8 - - (2)$ $2x+1.2y=-1.8--(2)$

in matrix form

$((5,3),(2,1.2))((x),(y))=((-4.5),(-1.8))$

to use matrices we need the inverse of the $2xx2$ matrix

to do this we need its determinant so we will do this first

$Delta=|(5,3),(2,1.2)|$

$=5xx1.2-2xx3$

$=6-6=0$

$Delta=0:.$ the inverse does not exist, so there are no solutions to the equations.

In fact eqn $(1)=2.5xx$ eqn $(2)$ which means they are parallel lines and do not intersect

How do you solve 5x + 3y = -4.55x+3y=−4.55x + 3y = -4.5 and 2x + 1.2y = -1.82x+1.2y=−1.82x + 1.2y = -1.8 using matrices?