Solving 11th grade math problem 2:
Solve the given mathematical linear equation and find the values of the given variables.
x + 3y + 5z = 18
x + 5y + 3z = 18
3x + y + 5z = 18
Solution:
Let as the given equations be identified as follows.
x + 3y + 5z = 18 ----------- (i)
x + 5y + 3z = 18 ----------- (ii)
3x + y + 5z = 18 ----------- (iii)
Consider the above given equations (i) and (ii). Subtracting the equation (i) and (ii) we get
x + 3y + 5z = 18
x + 5y + 3z = 18
-2y – 2z = 0 ------------------ (iv)
Consider the above given equations (ii) and (iii). In the equation (ii) multiply with a numerical 3, we get
3x + 15y + 18z = 54
Subtracting the equation (ii) and (iii) we get
3x + 15y + 18z = 54
3x + y + 5z = 18
14y + 4z = 36------------------- (v)
Consider the above equations (iv) and (v). In the equation (iv) multiply with the numerical 7, we get
-14y - 14z = 0
Subtract the equation (iv) and (v) we get
-14y - 14z = 0
14y + 4z = 36
18y = 36
Y = 2
Substitute y = 2 in (v) we get
14(2) + 4z = 36
28 + 4z = 36
z = 2
Substitute z = 2, y = 2 in (iii) we get
3x + 2 + 10 = 36
3x + 12 = 36
z = 2
Answers of a given algebraic variables are x = 2, y = 2, z = 2.
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