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Let's look at the second equation
Multiply both sides of the second equation by the LCD 6
So our new system of equations is:
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
to some equal number, we could try to get them to the LCM.
Since the LCM of
, we need to multiply both sides of the top equation by
and multiply both sides of the bottom equation by
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
Divide both sides by
to isolate y
Now plug this answer into the top equation
to solve for x
Start with the first equation
Subtract 0 from both sides
Combine like terms on the right side
So our answer is
which also looks like
Now let's graph the two equations (if you need help with graphing, check out this solver
From the graph, we can see that the two equations intersect at
. This visually verifies our answer.
(green) and the intersection of the lines (blue circle).