Question

Solve the following system of equations using the

Tons using the Gaussian Method of elimination.
x - 2y + z = 6
3x + y -z = 7
4x - y + 2z = 15

Use the guide line in the photo to follow the steps how todo it

Answer 1

x = 3, y = - 1, z = 1

Explanation:

listing the coefficients

1 - 2 1 6 ← R1

3 1 - 1 7 ← R2

4 - 1 2 15 ← R3

We require the first entry in R2 to be 0 while retaining R1 and the first 2 entries of R3 to be 0, thus

R2 - 3R1 and R3 - 4R1

1 - 2 1 6 ← R1

0 7 - 4 - 11 ← R2

0 7 - 2 - 9 ← R3

Now R3 - R2

1 - 2 1 6 ← R1

0 7 - 4 - 11 ← R2

0 0 2 2 ← R3

From R3

2z = 2 ⇒ z = 1

Substitute z = 1 into R2

7y - 4(1) = - 11

7y - 4 = - 11 ( add 4 to both sides )

7y = - 7 ⇒ y = - 1

Substitute y = - 1, x = 1 into R1

x - 2(- 1) + 1 = 6

x + 2 + 1 = 6

x + 3 = 6 ( subtract 3 from both sides )

x = 3

Solution is (3, - 1, 1 )