Estimate the solution to the system of these linear equations based on the graph.

Question

y = 2x + 3
y = 1/2x + 6

Answer 1

Based on the graph, it appears that the two lines intersect at a point approximately (x, y) = (0.5, 4).

Answer 2

Estimate the solution to the system of these linear equations based on the graph.

y = −x + 6

y = 3x − 2

Answer 3

Based on the graph, it appears that the two lines intersect at a point approximately (x, y) = (2, 4).

Answer 4

Determine the number of solutions to this system of linear equations:

2x + y = 6
4x + 2y = 8

Answer 5

To determine the number of solutions to this system of linear equations, we can write the second equation in terms of y:

4x + 2y = 8
Dividing both sides by 2:
2x + y = 4

Now, we can compare the two equations:
2x + y = 6
2x + y = 4

These two equations represent two parallel lines since they have the same slope (2) and different y-intercepts (6 and 4). Since two parallel lines never intersect, there are no solutions to this system of linear equations.