use the matrix tool to solve the system of equations choose the correct ordered pair 4x-7y=-12 -2x+6y=11
In google paste:
matrix system of equations solver 2x2
When you see list of results click on:
2x2 System of Equations - Solver that Shows Steps - MathPortal
When page be open set:
4x-7y=-12
-2x+6y=11
Click:
Solve by using Cramer's rule
then click:
Solve system
You will see solution step-by-step
No idea what "matrix tool" you have available, but I would just double the 2nd, then add
to eliminate the x's and you got y. No fancy smancy tool needed here.
To solve the system of equations using the matrix method, we will represent the system in matrix form and then use matrix operations to solve for the values of x and y.
First, let's write down the augmented matrix for the system of equations:
| 4 -7 | -12 |
| -2 6 | 11 |
Next, we will perform row operations to put the augmented matrix in row-echelon form:
1. Multiply the first row by -1/4 and replace the first row with the result:
| 1 7/4 | 3 |
| -2 6 | 11 |
2. Add 2 times the first row to the second row and replace the second row with the result:
| 1 7/4 | 3 |
| 0 37/2 | 17 |
3. Multiply the second row by 2/37 and replace the second row with the result:
| 1 7/4 | 3 |
| 0 1 | 34/37 |
Lastly, we will perform back substitution to find the values of x and y:
From the second row, we can conclude that y = 34/37.
From the first row, we can substitute the value of y to find x:
1 + (7/4) * (34/37) = 3
Simplifying the expression further:
1 + (7*34)/(4*37) = 3
(37/37) + (238/37) = 3
(37 + 238)/37 = 3
275/37 = 3
Therefore, the correct ordered pair that solves the system of equations is (x, y) = (275/37, 34/37).
To solve the given system of equations using matrices, we can represent the system in matrix form and then use matrix operations to find the solution. Here's how you can do it step by step:
Step 1: Write the system of equations in matrix form.
The system of equations is:
4x - 7y = -12 (equation 1)
-2x + 6y = 11 (equation 2)
To represent this system in matrix form, we can use the coefficients of the variables and the constants on the right side. Set up a matrix equation in the form Ax = B, where A is the matrix of coefficients, x is the matrix representing the variables, and B is the matrix representing the constants.
⎡ 4 -7 ⎤ ⎡ x ⎤ ⎡ -12 ⎤
⎢ ⎥ ⎢ ⎥ = ⎢ ⎥
⎣ -2 6 ⎦ ⎣ y ⎦ ⎣ 11 ⎦
Step 2: Find the inverse of matrix A.
To solve for x, we need to find the inverse of matrix A. Calculate the inverse of matrix A (if it exists). If the inverse exists, we can multiply both sides of the equation by A^(-1).
Step 3: Multiply both sides by the inverse of A.
Remember that when we multiply both sides of the equation by the inverse of A, we need to perform matrix multiplication.
(A^(-1))(A)x = (A^(-1))B
Step 4: Solve for x.
Multiply the matrices (A^(-1)) and B using matrix multiplication to find the matrix x, which represents the solution to the system of equations.
x = (A^(-1))B
Step 5: Interpret the results.
Once you have the matrix x, you can interpret the values in the matrix as the solution to the system of equations. In this case, the values in the x matrix represent the values of x and y.
Now, I will perform these steps using the given system of equations.