How do you solve the system of equations by using substitution: y = x + 5 and y = 2x - 7?

1 Answer

Answer:

Solve the first equation for x, substitute into the second equation, and get the answer of #x=12# and #y=17#

Explanation:

To solve using substitution, we'll take one of the equations (the first one - it's a very simple one), solve for x, and then substitute it into the second one.

So let's first take #y=x+5# and solve for #x#:

#y=x+5# - subtract 5 from both sides and we get

#y-5=x#

And now we can substitute that into the 2nd equation:

#y=2x-7#
#y=2(y-5)-7#

and let's simplify

#y=2y-10-7# - we can subtract #2y# from both sides and combine terms
#-y=-17#
#y=17#

We can now substitute the y value back into the given equations and find the x value:

#y=x+5#
#17=x+5#
#x=12#

#y=2x-7#
#17=2x-7#
#24=2x#
#x=12#

And we're done! #x=12# and #y=17#