# Each equation in a system of linear equations has infinitely many ordered-pair solutions.Determine whether the statement makes sense or does not make sense, and explain your reasoning.

Each equation in a system of linear equations has infinitely many ordered-pair solutions.Determine whether the statement makes sense or does not make sense, and explain your reasoning.
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Step 1
A system of linear equations usually contains set of two linear equation.
System of linear equations can have unique solution, infinitely many solutions or no solutions.
If lines intersect at one point then there will be unique solution.
If lines coincide with each other then there will be infinitely many solution.
If lines are parallel then there will be no solution.
Suppose if a system has linear equations as:
${a}_{1}x+{b}_{1}y+{c}_{1}=0$
${a}_{2}x+{b}_{2}y+{c}_{2}=0$
System will have unique solution if:
$\frac{{a}_{1}}{{a}_{2}}\ne \frac{{b}_{1}}{{b}_{2}}$
Step 2
No solution if:
$\frac{{a}_{1}}{{a}_{2}}=\frac{{b}_{1}}{{b}_{2}}\ne \frac{{c}_{1}}{{c}_{2}}$
Infinitely many solutions if:
$\frac{{a}_{1}}{{a}_{2}}=\frac{{b}_{1}}{{b}_{2}}=\frac{{c}_{1}}{{c}_{2}}$
Therefore, it is not necessay that each equations in system of linear equations has infinitely many solutions.
Hence, given statement doesn't make any sense.

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