How do I find the Y coordinate? #y = -2x+9# and #-x-y=-1#

1 Answer
Mar 22, 2018

Answer:

This is a system of simultaneous equations.

#y=-7#

Explanation:

Call the two equations:

Equation 1: #y=-2x+9#

Equation 2: #-x-y=-1#

Multiply both sides of Equation 2 by #-1#:

#x+y=1#

Subtract #y# from both sides:

#x=1-y#

Now, we can substitute this value of #x#, in terms of #y#, into Equation 1 where we see #x# in it:

#y=-2(1-y)+9#

Multiply out the parentheses:

#y=-2+2y+9#

Collect like terms (which involves subtracting #2y# from both sides):

#-y=7#

Multiply both sides by #-1#:

#y=-7#

We could also solve to find the value of #x#, but we are not asked to do so.

It's worthwhile and interesting to realise that these two equations are the equations of straight lines, and the #x# and #y# values in the solution are the coordinates of the point where the two straight lines cross.