Question

Consider the system of equations.

Answer 1

The solution to the system of equations x + 2y = 1  and -3x-2y = 5 is:

x  = -3,  y = 2

The given system of equations:

x  +  2y  =  1............(1)

-3x - 2y  =  5..........(2)

This can be written in matrix form as shown:

$\left[\begin{array}{ccc}1&2\\-3&-2\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}1\\5\end{array}\right]$

Find the determinant of $\left[\begin{array}{ccc}1&2\\-3&-2\end{array}\right]$

$\triangle = 1(-2) - 2(-3)\\\triangle = -2+6\\\triangle = 4$

$\triangle_x = \left[\begin{array}{ccc}1&2\\5&-2\end{array}\right]\\\triangle_x = 1(-2)-2(5)\\\triangle_x = -2-10\\\triangle_x =-12$

$\triangle_y = \left[\begin{array}{ccc}1&1\\-3&5\end{array}\right]\\\triangle_y = 1(5)-1(-3)\\\triangle_y = 5 + 3\\\triangle_y =8$

$x = \frac{\triangle_x}{\triangle} \\x = \frac{-12}{4} \\x = -3$

$y = \frac{\triangle_y}{\triangle} \\y = \frac{8}{4} \\y = 2$

The solution to the system of equations x + 2y = 1  and -3x-2y = 5 is:

x  = -3,  y = 2

Learn more here: brainly.com/question/4428059