Question

X+y=3 x-y=1 find the Find the determinants

Answer 1

• D = -2
• Dx = -4
• Dy = -2

Explanation:

System Determinant

The determinant of the system is the determinant of the matrix of coefficients:

`D=\left|\begin{array}{cc}1&1\\1&-1\end{array}\right|=(1)(-1)-(1)(1)=-2`

X Determinant

This is the determinant of the matrix with the x-coefficients replaced by the constants.

`D_x=\left|\begin{array}{cc}3&1\\1&-1\end{array}\right|=(3)(-1)-(1)(1)=-4`

Y Determinant

This is the determinant of the matrix with the y-coefficients replaced by the constants.

`D_y=\left|\begin{array}{cc}1&3\\1&1\end{array}\right|=(1)(1)-(3)(1)=-2`

_____

This problem didn't ask, but the solution is ...

x = Dx/D = -4/-2 = 2

y = Dy/D = -2/-2 = 1

(x, y) = (2, 1)