Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Consider the system of equations.


x+2y=1

−3x−2y=5


How do you solve the system of equations with Cramer's rule?


Drag a value or determinant expression into each box to correctly solve the system using Cramer's rule.

Sagot :

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

Learn more here: https://brainly.com/question/4428059