Question

If a system of equations has no solution, what does the graph look like? *



two lines graphed on top of each other

two parallel lines

two lines with one intersection

None of these​

Answer 1

Answer:

two parallel lines

Step-by-step explanation:

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Answer 2

Answer:

If a system of equations has no solution, then the lines are parallel lines.

Step-by-step explanation:

For any pair of linear equations,

$a_1x+b_1y+c_1=0$

$a_2x+b_2y+c_2=0$

1) Two lines graphed on top of each other.

It is also called the coincident lines.

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

Then, the system of linear equations has infinitely many solution.

And the lines are coincident lines.

2) Two parallel lines

When $\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}$.

Then, the system of linear equations has $no$ solution.

And the graph of the equations look likes the parallel lines.

3) Two lines with one intersection

When $\frac{a_1}{a_2}\neq \frac{b_1}{b_2}$.

Then, the system $of$ linear equations has unique solution.

And the graph of the equations are intersecting lines.

Thus, the graph of the equations must be parallel lines.

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