Question

How many solutions does this system of equations have?

exactly two
none
infinitely many
exactly one

Graph of a system of linear equations. Equation 1 is 3x plus 2y equals 6. Equation 2 is negative 4x plus 5y equals 15. The graphs intersect at a point.

Answer 1

Answer: exactly one solution

Explanation: Because the two lines only cross at one point and will never cross again

Answer 2

exactly one

Explanation:

The system of linear equations have:

one solution, infinitely many solutions or no solution.

One solution if the lines intersect.

Infinitely many solutions if the lines are the same (overlap)

There is no solution if the lines are parallel (they do not have a common point).

In the graph, two lines intersect. Therefore, the system of equations has one solution (0, 3).