How do you solve #y=2x+9# and #y=7x+10# using substitution?
Take the first equation and substitute for
now we substitute this value back into the first:
Here is another way of thinking about what is given....
The answer is the same as given by the previous contributor.
Both equations are in the form
In other words we have been given two different ways of writing
The two values for
Therefore the other parts of each equation must be equal to each other as well, leading to
I tend to regard this method as 'equating', rather than substitution.
This now gives an equation with one variable and it can be solved.
Once a value for
The second substitution acts as a check to ensure that the answers are correct.
Remember that from a graphical point of view, solving the equations of two straight lines simultaneously, gives the point of intersection of the two lines.
This concept is extremely useful and important.