Question

Solve the system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set y = t and solve for x in terms of t.) −3x + 5y = −19 3x + 4y = 1 4x − 8y = 28

Answer 1

Answer:

x = 3 and y = -2

Step-by-step explanation:

We have the following system:

-3 5 | 19

3  4  | 1

4 -8 | 28

We divide the first row by -3 and it would be:

1 -1.67 | 6.33

3   4    | 1

4  -8    | 28

Now, we multiply by 3 and subtract the second row and we have:

1 -1.67 | 6.33

0     9 | -18

4    -8 | 28

Now, we multiply by 4 and subtract the third row and we have:

1 -1.67 | 6.33

0    9   | -18

0 -1.33 | 2.67

divide the second row by 9:

1 -1.67  | 6.33

0    1    | -2

0 -1.33 | 2.67

multiply the second row by 1.33 and add it to the third row and it remains:

1 -1.67 | 6.33

0    1   | -2

0   0   | 0

multiply the second row by 1.67 and add it to the first row and we have:

1 0  | 3

0 1  | -2

0 0 | 0

Therefore, from here we can deduce that x = 3 and y = -2