finding the answer using MATRICES!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
To begin, we must first create two matrices from the given system of equations. One of those matrices is referred to as the coefficient matrix. It is called the coefficient matrix because it is created by using the coefficients of the variables involved. The second matrix we will create is called the constant matrix. It is created from the constants on the right side of the equal signs. The coefficient matrix will be represented by A, while the constant matrix will be represented by B.
Finding the coefficient and constant matrix!!!!!!!!!!!!!!!!!!!!!!!
Equations:
x+y=87
1.5x+0.5y=78.5
Coefficient Matrix: Constant Matrix:
1 1 87
1.5 0.5 78.5
Finding the inverse then multiplying it!!!!!!!!!!!!!!!!!!!!
To use these matrices to solve the system of equations, we need to find the inverse of Matrix A and multiply that answer by Matrix B. The two numbers of the final matrix will be our solution.
A-1 x B= 35
52
Check your answers!!!!!!!!!!!!!!!!!!!!!!!!
1.5x+50y=78.5
1.5(35)+50(35)=78.5
52.5+26=78.5
and....
x+y=87
35+52=87.
Finding the coefficient and constant matrix!!!!!!!!!!!!!!!!!!!!!!!
Equations:
x+y=87
1.5x+0.5y=78.5
Coefficient Matrix: Constant Matrix:
1 1 87
1.5 0.5 78.5
Finding the inverse then multiplying it!!!!!!!!!!!!!!!!!!!!
To use these matrices to solve the system of equations, we need to find the inverse of Matrix A and multiply that answer by Matrix B. The two numbers of the final matrix will be our solution.
A-1 x B= 35
52
Check your answers!!!!!!!!!!!!!!!!!!!!!!!!
1.5x+50y=78.5
1.5(35)+50(35)=78.5
52.5+26=78.5
and....
x+y=87
35+52=87.