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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