Question

How to do substitution or elimination

Answer 1

I: y=(1/2)x+5
II: y=(-3/2)x-7

substitution:
fancy word for insert the definition of one variable in one equation into the other
-> isolate a variable, luckily y is isolated (even in both equations) already
-> substitute y of II into I (=copy right side of II and replace y in I with it):

(-3/2)x-7=(1/2)x+5
-3x-14=x+10
-3x-24=x
-24=4x
-6=x

-> insert x back into I (or II):
y=(1/2)x+5
=(1/2)*(-6)+5
=-3+5=2

elimination: subtract one equation from the other to eliminate a variable, again y is already isolated->no extra work required

I-II:
y-y=(1/2)x+5-[(-3/2)x-7]
0=(1/2)x+5+(3/2)x+7
0=(4/2)x+12
-12=2x
-6=x

-> insert x back into I (or II):
y=(1/2)x+5
=(1/2)*(-6)+5
=-3+5=2