Linear equation consists of variables, coefficients and constants that describes an expression for certain mathematical aspects. However these equations plays a crucial role in various fields such as science, engineering and economics.
In this post, let's see how we can solve the three variable linear equations in 3 different methods.
x + 3y - 5z = 7 ------------(1)
3x - 7y + 9z = 12 -----------(2)
2x + 4y - z = 9 -----------(3)
Method-1 : Matrix Method Using Cramer's Rule
Method-2 : By Solving Equations
From (1), x = 7 - 3y + 5z -----------(4)
Using equation (4) in equations (2) and (3) we get,
3(7 - 3y + 5z) - 7y + 9z = 12------- From (2)
21 - 9y + 15z -7y +9z =12
-16y + 24z = -9 ------(5)
2(7 - 3y + 5z) + 4y - z = 9-------- From (3)
14 -6y +10z +4y -z = 9
-2y +9z = -5-------(6)
Solving (5) and (6) we get,
y = -0.4062, z = -0.645
Now using the values of y and z in equation (4) we get value of x.
x = 7 - 3(-0.4062) + 5(-0.645)
x = 4.99
Method-3 : By Equating The Row Values To Zero
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