Respuesta :
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:
[tex]\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][/tex]
Find the determinant of [tex]\left[\begin{array}{ccc}1&2\\-3&-2\end{array}\right][/tex]
[tex]\triangle = 1(-2) - 2(-3)\\\triangle = -2+6\\\triangle = 4[/tex]
[tex]\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[/tex]
[tex]\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[/tex]
[tex]x = \frac{\triangle_x}{\triangle} \\x = \frac{-12}{4} \\x = -3[/tex]
[tex]y = \frac{\triangle_y}{\triangle} \\y = \frac{8}{4} \\y = 2[/tex]
The solution to the system of equations x + 2y = 1 and -3x-2y = 5 is:
x = -3, y = 2
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