Solve by using matrix method
6x+8y = 30
9x+5y =42
Solution
Writing the equation in the matrix form
AX = B
A =
6
9
8
5
X =
x
y
B =
30
42
6
9
8
5
x
y
=
30
42
X = A⁻¹ B.
So, now we find A⁻¹.
|A| =
6
9
8
5
= 6×5 - 9×8 = 30 - 72 = -42
As determinant of the matrix ≠ 0. Hence its inverse exists.
Inverse of matrix A = A-¹
=
1
|A|
5
-9
-8
6
=
1
-42
5
-9
-8
6
∴ Inverse matrix of A = A-¹ =
-0.119
0.214
0.19
-0.143
A-¹ × B =
-0.119
0.214
0.19
-0.143
×
30
42
A-¹ × B =
(-0.119)×30+0.19×42
0.214×30+(-0.143)×42
A-¹ × B =
-3.57+7.98
6.42-6.006
∴ A-¹ B =
4.41
0.41
∴x = 4.41
∴y = 0.41
∴y = 0.41
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