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Write a system of equations that satisfies each condition below: No solution The slope of one of the equations is 3

User Hasankzl
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1 Answer

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We can write a system of equations that satisfy this two conditions:

- No solution

- The slope of one of the equations is 3.

We start with the second condition: we can write the equation of a line with slope 3 as:


y=3x+b

Then, we can assign any value to the y-intercept b, for example b=0, and we have the first equation as:


y=3x

For the system to have no solution, the two equations have to be parallel lines that are not equal.

We can do it by writing a line equation with the same slope m=3, so they are parallel, but with a different y-intercept, like b=1.

Then, we have the equation:


y=3x+1

If we graph both equations, we get:

The two lines do not intersect for any finite values of x and y, so the system has no solution.

Answer:

The system of equations:


\begin{gathered} y=3x \\ y=3x+1 \end{gathered}

has no solution and a equation with slope 3.

Write a system of equations that satisfies each condition below: No solution The slope-example-1
User Jerry Chen
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