5x+3y=13

4x+7y=-8
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solve 5x=3Y=13 and 4x+7y=-8 using matrices

 

Let A be a 2x2 matrix such that A = |a b|

                                                         |c d|

Then the inverse of A is given by,

A^(-1) = (1/det(A)) * |d -b|

                                |-c  a|

Our equations are:

5x + 3y = 13     | 5  3|| x | = |13|

4x +  7y = -8     | 4  7|| y | = | -8|

 

Which in matrix form is: AX = R,

Where X is the unknowns matrix, [x  y], and R is the constants matrix [13  -8].

 

Our determinant is A = |5  3|

                                     |4  7|

det(A) = ad – bc = 5*7 – 3*4 = 35 – 12 = 23

det(A) = 23

using the definition for A^(-1) above,

A^(-1) = (1/23)*|7  -3|

                         |-4 5|

And,

X = A^(-1) * R = (1/23)*|7  -3| * |13|  =  (1/23)*|91 + 24| = (1/23)*|115| = | 5|

                                     |-4  5|    | -8|                |-52 -40|                |-92|     |-4|

X = | 5|

       |-4|

Solution: x = 5, y = -4

 

by Level 11 User (81.5k points)

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