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# 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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Equations asked 2020-11-08
Solve the following systems of equations by using the addition (elimination) method.
x+2y=2 and -3x-6y=-6

## Answers (1) 2020-11-09
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.$$\displaystyle\frac{{1}}{{-{3}}}=\frac{{2}}{{-{6}}}=\frac{{2}}{{-{6}}}={k}$$
Step 4
Hence, the system of equations have infinite solutions.
Therefore, substituting x=k in (1) gives
k+2y=2
2y=2-k
$$\displaystyle{y}=\frac{{{2}-{k}}}{{2}}$$
(Hence for x = k, $$\displaystyle{y}=\frac{{{2}-{k}}}{{2}}$$ is required solution for the system of equations.)

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