Solve the system of equations using either the substitution method or the multiplication/addition methodusing his given
3x+2y=14
2x-4y=4

6x+4y=28
2x-4y=4
8x = 32
x = 4
2y = 14 - 12 = 2
y = 1
(x , y) = (4 , 1)


Question:How can check your solution by writing the system as a matrix equation and using the inverse matrix?.

Final answer:

To check the solution, represent the system of equations as a matrix equation, find the inverse of the coefficient matrix, and multiply both sides of the equation by the inverse.

Explanation:

To check the solution by writing the system as a matrix equation and using the inverse matrix, we need to represent the system of equations as a matrix equation. Let's consider the given system of equations:

3x + 2y = 14

2x - 4y = 4

To do this, we can write the coefficients and constants of the system of equations as matrices:

[3 2] [x] = [14]

[2 -4] [y] = [4]

Now, we can write the system of equations as a matrix equation: AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.

Next, we need to find the inverse of matrix A. If the inverse exists, we can multiply both sides of the matrix equation by the inverse of A to find the solution for X.

If we find the inverse of A and multiply both sides of the equation by the inverse, we get:

X = A-1B

Substituting the values of A-1 and B, we can find X, which represents the solution to the system of equations. Therefore, we can check our solution by writing the system as a matrix equation and using the inverse matrix.

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