Write the system of equations as an augmented matrix. Then solve for x and y.
5x-3y=-34
10x−5y=−65
5 -3 -34
10 -5 -65
(-5, +3)
see
http://matrix.reshish.com/gaussSolution.php
Click on Gauss Jordan there of course.
Oh, and you might want to click on "very detailed solution" :)
To write the system of equations as an augmented matrix, we can represent the coefficients of the variables and the constants as follows:
5 -3 | -34
10 -5 | -65
The left side of the augmented matrix contains the coefficients of the variables (in this case, x and y), and the right side contains the constants from the equations.
To solve for x and y, we can use the method of Gaussian elimination or row reduction. Let's go through the steps using the matrix:
Step 1: Perform row operations to create a leading 1 in the first row. Multiply the first row by 2/5:
1 -3/5 | -34/5
10 -5 | -65
Step 2: Eliminate the coefficient below the leading 1 in the first row by multiplying the first row by -10 and adding it to the second row:
1 -3/5 | -34/5
0 1 | -3/5
Step 3: Perform row operations to create a leading 1 in the second row. Multiply the second row by 5:
1 -3/5 | -34/5
0 1 | -3/5
Step 4: Eliminate the coefficient above the leading 1 in the second row by multiplying the second row by 3/5 and adding it to the first row:
1 0 | -17/5
0 1 | -3/5
The matrix is now in row-echelon form. The solutions for x and y can be read from the matrix, where the values on the right side represent x and y, respectively. So the solution is:
x = -17/5
y = -3/5