Both equations are already set equal to a constant. Notice that the coefficient of
in the second equation, –1, is the opposite of the coefficient of
in the first equation, 1. We can add the two equations to eliminate
without needing to multiply by a constant.
Now that we have eliminated
we can solve the resulting equation for
Then, we substitute this value for
into one of the original equations and solve for
Using the addition method when multiplication of one equation is required
Solve the given system of equations by the
addition method .
Adding these equations as presented will not eliminate a variable. However, we see that the first equation has
in it and the second equation has
So if we multiply the second equation by
the
x -terms will add to zero.
Now, let’s add them.
For the last step, we substitute
into one of the original equations and solve for
Our solution is the ordered pair
See
[link] . Check the solution in the original second equation.
Using the addition method when multiplication of both equations is required
Solve the given system of equations in two variables by addition.
One equation has
and the other has
The least common multiple is
so we will have to multiply both equations by a constant in order to eliminate one variable. Let’s eliminate
by multiplying the first equation by
and the second equation by
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