Can someone refresh my mind on Algebra? Please help with equations, at what point do these two intersect? 2x-y=1 3x=y-6 Thanks

Question

Can someone refresh my mind on Algebra? Please help with equations, at what point do these two intersect?   2x-y=1    3x=y-6    Thanks

anonymous · Answer

There are two different methods that one can apply here:

First is substitution:

Solve one of the equations by isolating one variable and plug into the other

$$2x-y=1  $$ -- this can be arranged to

$$y=2x-1 $$-- now plug it into the other equation

$$3x= (2x-1)-6$$-- solving for x we get

x= -7   -- plug back into any equation to get y
y= -15

anonymous · Answer

The next method is Elimination:

the key here is to make ONE of the variables cancel out by adding or subtracting the equations.

since there is a -y and a -y in both equations i can simply subtract the two equations together

2x-y=1   -- first minus the second 
3x-y=-6

-x=7 -- which is simplified to

x=-7  -- now plug back in to find y
y=-15

there is another method you leaner later where you learn matrices and reduce to something called row echelon form and it gives you the answer but that is linear algebra not regular algebra, so that is just fun info.