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Suppose you have n linear equations in n unknown variables.
Take any equation and rewrite it to make one of the variables the subject of the equation. That is, express that variable in terms of the other (n-1) variables. For example, x + 2y + 3z + 4w = 7
can be rewritten as x = 7 - 2y - 3z - 4w
Then, in the other (n-1) equations, plug in that value for the variable and simplify (collect like terms). You will end up with (n-1) equations in (n-1) unknown variables. Repeat until you have only one equation in 1 variable.
That gives you the value of one of the variables. Plug that value into one of the equations from the previous stage. These will be one of two equations in two variables. That will give you a second variable. Continue until you have all the variables.
There are simpler methods using matrices but you need to have studied matrices before you can use those methods.
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What is indicated by the occurrence of a false statement such as 0 equals 1 when you solve a system of two linear equations in two variables using substitution?
In that instance, it means that the lines never touch.
How do you decide whether to use elimination or subsitution to solve a three-variable system?
There is no simple answer. Sometimes, the nature of one of the equations lends itself to the substitution method but at other times, elimination is better. If they are non-linear equations, and there is an easy substitution then that is the best approach. With linear equations, using the inverse matrix is the fastest method.
When using the substitution method to solve a nonlinear system of equations you should first see if you can one variable in one of the equations in the system?
isolate
How do you work out the point of intersection without a graph?
You use algebra and solve the system(s) of equations using techniques such as elimination or substitution.
How would use solve the system of equation x plus 3y equals 23 by using substitution?
You'd need another equation to sub in
What is indicated by the occurrence of a false statement such as 0 equals 1 when you solve a system of two linear equations in two variables using substitution?
In that instance, it means that the lines never touch.
What is an advantage of using the method of substitution rather than using a graph or table to solve a system of linear equations?
You will obtain a more accurate answer than is possible using graphical methods. It's faster and less work than using a table.
What is the disadvantage of using the substitution method in solving linear equations rather than the graph method?
There are no disadvantages. There are three main ways to solve linear equations which are: substitution, graphing, and elimination. The method that is most appropriate can be found by looking at the equation.
How do you decide whether to use elimination or subsitution to solve a three-variable system?
There is no simple answer. Sometimes, the nature of one of the equations lends itself to the substitution method but at other times, elimination is better. If they are non-linear equations, and there is an easy substitution then that is the best approach. With linear equations, using the inverse matrix is the fastest method.
To solve the system given below using substitution it is best to start by solving the second equation for y?
True
When using the substitution method to solve a nonlinear system of equations you should first see if you can one variable in one of the equations in the system?
isolate
How can you solve a system of equations?
The answer depends on whether they are linear, non-linear, differential or other types of equations.
How do you work out the point of intersection without a graph?
You use algebra and solve the system(s) of equations using techniques such as elimination or substitution.
How do you solve Linear Equations with the substitution method?
You just plug in the value of the given variable. For example: y=3+2 2y=x (now you substitute y for 3+2) 2(3+2)=x (now solve the equation using distributive property) 6+4=x 10=x Tuhduh!! All done using the substitution property.
How would use solve the system of equation x plus 3y equals 23 by using substitution?
You'd need another equation to sub in
Translate this word problem as a system of equations and then solve using substitution?
A system of equations is two or more equations that share at least one variable. Once you have determined your equations, solve for one of the variables and substitute in that solution to the other equation.
When is it best to solve a systems of linear equations using elimination?
Elimination is particularly easy when one of the coefficients is one, or the equation can be divided by a number to reduce a coefficient to one. This makes substitution and elimination more trivial.
