Question

The graph shows two lines, A and B.

Part A: How many solutions does the pair of equations for lines A and B have? Explain your answer.

Part B: What is the solution to the equations of lines A and B? Explain your answer

Answer 1

A: 1 solution

B: (4,4) is the solution

Explanation:

They have different slopes so they're already different equations and because of that, they can only have one solution.

The intersection of the two lines is the solution since those coordinates satisfy both equations.

Answer 2

Part A

The solutions of a graphed pair of equations are the points of intersection - the points on the graph where the two lines cross each other. At this point, when inputting the same x-value into the 2 equations, the resulting y-values will also be the same.

Therefore, from inspection of the graph, there is one point of intersection, and so one solution.

The name for a system that has one solution and intersects at one point is Consistent Independent

Part B

From inspection of the graph, the point of intersection is (4, 4).

Therefore, the solution to the equations of line A and B is (4, 4).

Proof

• Equation of line B: y = x
• Equation of line A: y = -0.5x + 6

Using substitution:

⇒ x = -0.5x + 6

⇒ 1.5x = 6

⇒ x = 4

Substituting the found value of x into one of the equations to find y:

⇒ y = 4

Therefore, the solution is (4, 4)