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1. Plug in the coefficients from each equation into the coefficient matrix D.
2. Plug in the three different solutions into the solution matrix.
3. Substitute the variables into the three different equations and find the determinant of each one.
4. Then divide every single one by the determinant of D.

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4) multiply both sides of the matrix equation with the inverse of [A]
- solve for X
- simplify

0 3 pointer field goals
658 2 pointer field goals
353 free pointers

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Check that A=0, B=658, and C= 353 are correct by plugging them into both of the original points and shots equations.

A + B +C = 1011
0 + 658 + 353  = 1011
1011 = 1011

3A + 2B + C = 1669
3(0) + 2(658) + 353 = 1669
1669 = 1669

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3) solve for 'X' by finding the inverse of [A] with a calculator:

to input matrix in a graphic calculator:
- press 2nd, MATRIX, go right 3 times to EDIT
- enter a 3x3 matrix
- put in the values of the coefficient matrix

how to find the inverse of a 3x3 matrix in a graphing calculator
- press 2nd, MATRIX again
- press 1
- press x^-1
- ENTER

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Now, that we have the value of C, we can plug in this value into other equations to find the values of all the variables.

Plug in 353 for C:
A = 706 - 2C
A = 706 - 2(353)
A = 0

Plug in A and C to find B:
A + B + C = 1011
0 + B + 353 = 1011
B = 658

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Isolate 1 variable to substitute in the second equation. In this case, it would be easiest to solve for A in the first equation.

A + 2C = 706
A = 706 - 2C

Substitute:
3 (706 - 2C) + 3C = 1059
2118 - 3C= 1059
1059 = 3C
353= C

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Substitute B with C + 305:

Shots: A + B + C = 1011
A + (C+305) + C = 1011
A + 2C + 305 (-305) = 1011 (-305)
A + 2C = 706

Points: 3A + 2B + C = 1669
3A + 2(C+305) + C = 1669
3A + 3C + 610 = 1669
3A + 3C = 1059

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We prefer SUBSTITUTION because this method is the most familiar to the everyday person. Matrices can be complicated and easily messed up. One simple mistake can effect the end result of your question a lot more than a mistake made with substitution. Using substitution can also be checked easily.

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1) rewrite all equations so that the variables are one side:

A + B + C = 1011
3A + 2B + C = 1669
0A + -B + C  = -305

2) write the coefficient matrix and the solution matrix into a matrix equation:

AX = B

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Shots: A + B + C = 1011
Points: 3A + 2B + C = 1669
Relationship between 2-point goals and 1 point free throws: B = C +305

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During the 2004-2005 NBA season, Shaquille O' Neal scored 1669 points while making 1011 shots. Shaq's points were a combination of 3-point field goals, 2-point field goals, and 1-point free throws. He made 305 more 2-point field goals than free throws.

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A = Number of 3-point field goals
B = Number of 2-point field goals
C = Numbrt of 1- point free throws

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We chose this method over elimination because we were already given the relationship between 2-point goals and 1 point free shows. Since the equation (B=C+305) already has 1 variable isolated, it would be more efficient to plug in and substitute the value of B with C+305  into the shots and points equations so that we could solve with 2 variables instead of 3.