Solve the following system of simultaneous linear equations:

2x + y + z = 10

3x + 2y + 3z= 18

x + 4y + 9z = 16

1 Answers

To solve these equations, follow these steps.

**Step1: **

Multiply the first equation to eliminate x successively by –3/2 and –1/2 and add it to the second and third equations respectively, we get

(1/2) y + (3/2)z = 3 …….(1)

(7/2) y + (17/2) z = 11 ……..(2)

**Step2: **

Now to eliminate y from equation 1 and 2, multiply equation 1 by –7 and add it to equation 2, we get

–2z = –10

z = 5

**Step3: **

Now, substitute the value of z in equation 1, we get value of y, i.e.

y + 15 = 6

y = –9

Now, again substitute the value of y and z in given equations, we get the value of y i.e.

2x – 9 + 5 = 10

2x – 4 = 10

2x = 14

x = 7

**Answer: x = 7, y = –9 and z = 5**

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