Question

Part A: how many solutions dose the pair of equations for lines A and B have?

Answer 1

Any line can be expressed in the form y=mx+b where m is the slope and b is y intercept.

Two lines can either be parallel ,overlap or meet at one point .Let us look at different cases :

1)When two lines are parallel they do not intersect at any point and hence the system of equations have no solution.

2) When two lines overlap each other then the two lines touch each other at infinite number of points and we say the system of equations have infinite solutions.

3) When two lines intersect each other at one point we say the system of equation has one solution.

Part A:

The given lines are intersecting at one point so we have one solution.

Part B:

The point of intersection is the solution to the system of equations .In the graph the point of intersection of the lines is (4,4)

Solution is (4,4)

Answer 2

Part A: The number of solutions for a set of linear equations (in this case only two of them, represented as two lines) is the number of points of intersection. For linear equations in 2-dimensions the only possible answers are zero, one and infinity. In this case it is clearly one.

Part B: By inspection, the point of intersection, and thus the solution to the system of equations, is (4,4).