# Solve the following systems of equations by using the addition (elimination) method. x+2y=2 and -3x-6y=-6

Solve the following systems of equations by using the addition (elimination) method.
x+2y=2 and -3x-6y=-6
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Yusuf Keller
Step 1
The given system of equations are
x+2y=2.....(1)
and -3x-6y=-6
Step 2
To find: The solution for the given equations.
Step 3
Since, the given two equation are same just by a factor of multiple of -3 in second equation.
Hence, the given system of equations has infinitely many solutions.
ie.$\frac{1}{-3}=\frac{2}{-6}=\frac{2}{-6}=k$
Step 4
Hence, the system of equations have infinite solutions.
Therefore, substituting x=k in (1) gives
k+2y=2
2y=2-k
$y=\frac{2-k}{2}$
(Hence for x = k, $y=\frac{2-k}{2}$ is required solution for the system of equations.)
Jeffrey Jordon