0
How do you solve systems of linear equations with three variables?
Wiki User
∙ 13y ago
You have to eliminate one variable between two equations at a time. For example:
5x + 2y + z = 10
10x - 2y - z = 12
10x - 4y + z = 14
You can add the first two equations together to get 15x = 22,
then divide by 15 to get x = 22/15.
Now combine the second and third equations:
10x - 2y - z = 12
10x - 4y + z = 14
20x - 6y = 26
Now you can plug 22/15 in for x. When you solve for y, you should have y = 5/9.
When you substitute y and z into any of the top three equations, you should find that z = 14/9.
You can check by plugging in 22/15 for x, 5/9 for y, and 14/9 for z in any of the top three equations, and they should fit perfectly.
In other words the solution is (22/15, 5/9, 14/9).
Wiki User
∙ 13y ago
Add your answer:
Earn +20 pts
How to solve linear Equations in 3 variables using Cramer's Rule?
Ask you math professor
What are two symbolic techniques used to solve a system of linear equations in two variables?
I have never seen the term 'symbolic' used in this way. There are 4 methods used to solve a system of linear equations in two variables. Graphing, Substitution, Elimination, and Cramer's Rule.
Solve linear equations with complex coefficients on both sides?
You would solve them in exactly the same way as you would solve linear equations with real coefficients. Whether you use substitution or elimination for pairs of equations, or matrix algebra for systems of equations depends on your requirements. But the methods remain the same.
What is -8t - 11x?
It is a linear expression in two variables. As an expression it cannot be solved. Furthermore, to solve equations in two variables you need at least two linear equations.
How do you work a simultaneous equation?
You cannot work a simultaneous equation. You require a system of equations. How you solve them depends on their nature: two or more linear equations are relatively easy to solve by eliminating variables - one at a time and then substituting these values in the earlier equations. For systems of equations containing non-linear equations it is simpler to substitute for variable expression for one of the variables at the start and working towards the other variable(s).
Is linear algebra and linear equations the same?
Linear Algebra is a branch of mathematics that enables you to solve many linear equations at the same time. For example, if you had 15 lines (linear equations) and wanted to know if there was a point where they all intersected, you would use Linear Algebra to solve that question. Linear Algebra uses matrices to solve these large systems of equations.
How can you solve a system of equations?
The answer depends on whether they are linear, non-linear, differential or other types of equations.
What does it mean by solving linear systems?
Solving linear systems means to solve linear equations and inequalities. Then to graph it and describing it by statical statements.
How to solve linear Equations in 3 variables using Cramer's Rule?
Ask you math professor
How do you solve x-y equals 13?
You need two independent linear equations to solve for two unknown variables.
What are two symbolic techniques used to solve a system of linear equations in two variables?
I have never seen the term 'symbolic' used in this way. There are 4 methods used to solve a system of linear equations in two variables. Graphing, Substitution, Elimination, and Cramer's Rule.
What does it mean to solve a system of linear equations?
Find values for each of the unknown variables (or at least as many as is possible for the system) that satisfy all the equations.
Solve linear equations with complex coefficients on both sides?
You would solve them in exactly the same way as you would solve linear equations with real coefficients. Whether you use substitution or elimination for pairs of equations, or matrix algebra for systems of equations depends on your requirements. But the methods remain the same.
What is -8t - 11x?
It is a linear expression in two variables. As an expression it cannot be solved. Furthermore, to solve equations in two variables you need at least two linear equations.
How do you work a simultaneous equation?
You cannot work a simultaneous equation. You require a system of equations. How you solve them depends on their nature: two or more linear equations are relatively easy to solve by eliminating variables - one at a time and then substituting these values in the earlier equations. For systems of equations containing non-linear equations it is simpler to substitute for variable expression for one of the variables at the start and working towards the other variable(s).
How do you solve a system of equation with 3 equations and 3 variables?
If you know matrix algebra, the process is simply to find the inverse for the matrix of coefficients and apply that to the vector of answers. If you don't: You solve these in the same way as you would solve a pair of simultaneous linear equations in two unknowns - either by substitution or elimination. For example, change the subject of one of the equations to express one of the variables in terms of the other two. Substitute this value into the other two equations. When simplified, you will have two linear equations in two variables.
How do you solve using elimination method 2x-y equals -2?
4
