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We will use an example to answer this question. Let's consider a system of linear equations.
${2x+y+8=122x+y+2=6 (I)(II) $
Note that both the $x-$ and the $y-$variables have the same coefficient in both equations. Thus, in order to use the elimination method, we will subtract Equation (II) from Equation (I).
$− 2x+y+82x+y+26 === 121616 $
We arrived to a true statement. Its truthfulness does not depend on any variable. Thus, any value for $x$ and $y$ will satisfy the statement. This happens when the two lines are coincidental and then the system has **infinitely many solutions.**

b

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Finally, to answer this question, we will use a third example.
${x−y+2=6-x+y+3=5 $
In this example the $x-$ and the $y-$variables have opposite coefficients. Therefore, to solve the system, we will add the equations.
$+ x−y+2-x+y+35 == = 6511 $
Since we know that $5 =11,$ we have a arrived at a false statement. There are no values for $x$ and $y$ that satisfy it. Thus, the system has **no solution.** This means the lines do not intersect. Every time we arrive to a false statement, the system has no solution.