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Start with the given system of equations:
Now in order to solve this system by using elimination/addition, we need to solve (or isolate) one variable. I'm going to solve for y.
In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for
, we would have to eliminate
(or vice versa).
So lets eliminate
. In order to do that, we need to have both
coefficients that are equal in magnitude but have opposite signs (for instance 2 and -2 are equal in magnitude but have opposite signs). This way they will add to zero. By adding to zero, they can be eliminated.
So to make the
coefficients equal in magnitude but opposite in sign, we need to multiply both
coefficients by some number to get them to an common number. So if we wanted to get
and
to some equal number, we could try to get them to the LCM.
Since the LCM of
and
is
, we need to multiply both sides of the top equation by
and multiply both sides of the bottom equation by
like this:
Multiply the top equation (both sides) by
Multiply the bottom equation (both sides) by
Distribute and multiply
Now add the equations together. In order to add 2 equations, group like terms and combine them
Combine like terms and simplify
Notice how the x terms cancel out
Simplify
Divide both sides by
to isolate y
Now plug this answer into the top equation
to solve for x
Start with the first equation
Plug in
Multiply
Multiply both sides by the LCM of 31. This will eliminate the fractions (note: if you need help with finding the LCM, check out this
solver)
Distribute and multiply the LCM to each side
Add 432 to both sides
Combine like terms on the right side
Divide both sides by 155 to isolate x
Reduce
So our answer is
and
which forms the ordered pair
)
(