Question

Michaela solved a system of linear equations that had no solution. One of the equations was x + y = 5. The other equation had a y-intercept of −2. What was the other equation?

Answer 1

We have a system of equations with no solutions.

One of the equations is:

x + y = 5.

Isolating y in one side of the equation, we get:

y = 5 - x

And the other equation has an y-intercept of -2, the equation can be written as:

y = a*x - 2.

Then the system will be:

y = -1*x + 5

y = a*x - 2

The solution of a system of equations is a point where the graphs of both functions intersect.

Then if both of these lines are parallel, the lines will never intersect, then the second equation must be parallel to the first one.

And two lines are parallel if they have the same slope.

Then the other equation will be:

y = -x - 2