to solve x + y = 3 , 3x - 2y = 4 by determinant method. find the value of D.
Answers
x+y=3
3x-2y=4
To solve this system, three determinants are created. One is called the denominator determinant, labeled D; another is the x‐numerator determinant , labeled D x; and the third is the y‐numerator determinant , labeled D y .
The denominator determinant, D, is formed by taking the coefficients of x and y from the equations written in standard form.
equation
D=|1 1l
|3 -2|
=(1×(-2))-(3×1)
=-2-3
=-5
The x‐numerator determinant is formed by taking the constant terms from the system and placing them in the x‐coefficient positions and retaining the y‐coefficients.
equation
Dx= |3 1|
|4 -2|
= (-2×3)-(4×1)
=(-6)-4
=-10
The y‐numerator determinant is formed by taking the constant terms from the system and placing them in the y‐coefficient positions and retaining the x‐coefficients.
equation
Dy=| 1 3|
| 3 4|
=(4×1)-(3×3)
=4-9
=-5
The answers for x and y are as follows: equation
The check is left to you. The solution is x =Dx/D=-10/-5=2. Y=Dy/D=-5/-5=1