Question

How do you solve `y=2x+9` and `y=7x+10` using substitution?

Answer 1

I found:
`x=-1/5`
`y=43/5`

Explanation:

Take the first equation and substitute for `y` into the second:
`color(red)(2x+9)=7x+10`
`5x=-1`
`x=-1/5`
now we substitute this value back into the first:
`y=-2(color(blue)(1/5))+9`
`y=43/5`

Answer 2

Here is another way of thinking about what is given....
The answer is the same as given by the previous contributor.

Explanation:

Both equations are in the form `y = ......`

In other words we have been given two different ways of writing `y`

The two values for `y` are the same, so `y = y`
Therefore the other parts of each equation must be equal to each other as well, leading to `7x + 10 = 2x + 9`

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 `x` has been found, it can be substituted into each of the given equations to find `y`.

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.