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

2 Answers
Apr 30, 2016

Answer:

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#

May 1, 2016

Answer:

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.