We are given two equations to solve for the variables a and b.
Let's write this system as a matrix equation.
6a+ 8b=5 10a-12b=2
⇕
6& 8 10& -12
a b =
5 2
A matrix equation like this can be solved using the inverse matrix.
MX=P ⟹ X=M^(-1)P
Use the determinant to find the inverse of a 2* 2 matrix.
M= 6& 8 10& -12
⇓
|M|= 6(-12)- 8( 10)=-152
⇓
M^(-1)=1/-152 -12& - 8 - 10& 6
Let's use this inverse to find the answer to the question.
The equality of these two matrices gives the solution of the equation system.
a&=0.5 b&=0.25
Checking Our Answer
How to use the calculator?
Graphing calculators can do the calculation for us.
First, we need to enter the coefficient matrix and the constant matrix in the memory of the calculator.
To do this, press 2ND, followed by x^(-1) to access the matrix menu. Then, scroll to the right until you reach the EDIT menu, choose to edit matrix A, and enter the coefficient matrix.
Go back to the matrix menu, and this time choose to edit matrix B and enter the constant matrix.
Once you have the matrices stored, you can use their names to find X=A^(-1)B.
