SOLUTION: Solve by using matrx 2x-y=-2 3x+4y=3

Question 821785: Solve by using matrx
2x-y=-2
3x+4y=3
Found 2 solutions by jsmallt9, ewatrrr:
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
There are several matrix-based methods for solving such a system. Please re-post your problem and specify which method should be used. (If "any" method may be used, then say so in your re-post and list the methods you have learned so the tutor can use a method you would have a chance of understanding.)
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!

Hi,
Solve by using matrx
2x-y=-2
3x+4y=3
x= ^-5⁄₁₁ and y= ¹²⁄₁₁ giving the ordered pair (-5/11, 12/11)

Solved by pluggable solver: Using Cramer's Rule to Solve Systems with 2 variables

First let . This is the matrix formed by the coefficients of the given system of equations.

Take note that the right hand values of the system are and which are highlighted here:

These values are important as they will be used to replace the columns of the matrix A.

Now let's calculate the the determinant of the matrix A to get . Remember that the determinant of the 2x2 matrix is . If you need help with calculating the determinant of any two by two matrices, then check out this solver.

Notation note: denotes the determinant of the matrix A.

---------------------------------------------------------

Now replace the first column of A (that corresponds to the variable 'x') with the values that form the right hand side of the system of equations. We will denote this new matrix (since we're replacing the 'x' column so to speak).

Now compute the determinant of to get . Once again, remember that the determinant of the 2x2 matrix is

To find the first solution, simply divide the determinant of by the determinant of to get:

So the first solution is

---------------------------------------------------------

We'll follow the same basic idea to find the other solution. Let's reset by letting again (this is the coefficient matrix).

Now replace the second column of A (that corresponds to the variable 'y') with the values that form the right hand side of the system of equations. We will denote this new matrix (since we're replacing the 'y' column in a way).

Now compute the determinant of to get .

To find the second solution, divide the determinant of by the determinant of to get:

So the second solution is

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Final Answer:

So the solutions are and giving the ordered pair (-5/11, 12/11)

Once again, Cramer's Rule is dependent on determinants. Take a look at this 2x2 Determinant Solver if you need more practice with determinants.

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