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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
