HELP ME is systems of linear equations and must be solved with the equalization method
Answers
Systems are relationships between two or more equations containing variables that we must find their values. We can do it through different methods, such as:
Elimination.
Equalization.
Substitution.
Gauss Jordan.
Graph.
The systems have only three types of solutions:
A single solution: the lines intersect at a single point, and the system is considered consistent.
Infinite solutions: they are the same line, and it is considered a consistent dependent system.
No solution: the lines are parallel, and it is considered an inconsistent system.
Answer and Explanation: 1
Assuming that the system has three equations of three variables, we can solve it with the following procedure:
First, identify the equations as
E
q
.
1
Eq.1,
E
q
.
2
Eq.2, and
E
q
.
3
Eq.3.
Extract two equations, e.g.,
E
q
s
.
1
Eqs.1 and
2
2, solve by elimination, leaving a fourth equation (
E
q
.
4
Eq.4) with two variables.
Take
E
q
s
.
1
Eqs.1 and
E
q
.
3
Eq.3, solve by elimination, leaving a fifth equation (
E
q
.
5
Eq.5) with two variables.
Make a system with Eqs.
E
q
s
.
4
Eqs.4 and
5
5, solve by elimination, equalization, or substitution, to find the value of one of the variables.
Substitute the value of the variable in
E
q
.
4
Eq.4 or
5
5, finding the value of the second variable.
Substitute the values of the variables found in
E
q
.
1
Eq.1,
2
2, or
3
3.
Perform the corresponding mathematical operations to find the value of the third variable.
With this procedure, we can solve a system of equations with three variables.