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

Nov 4, 2017

no solution, the lines are parallel .

#### Explanation:

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

$2 x + 1.2 y = - 1.8 - - \left(2\right)$

in matrix form

$\left(\begin{matrix}5 & 3 \\ 2 & 1.2\end{matrix}\right) \left(\begin{matrix}x \\ y\end{matrix}\right) = \left(\begin{matrix}- 4.5 \\ - 1.8\end{matrix}\right)$

to use matrices we need the inverse of the $2 \times 2$ matrix

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

$\Delta = | \left(5 , 3\right) , \left(2 , 1.2\right) |$

$= 5 \times 1.2 - 2 \times 3$

$= 6 - 6 = 0$

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

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