Question

Which of the points on the graph is a solution to the simultaneous inequalities y>3x+1 and y≤2x+5 ?

Answer 1

To find the points on the graph that satisfy both inequalities, we need to find the points that are above the line y=3x+1 and below or on the line y=2x+5.

We can start by graphing the two lines to see where they intersect.

The line y=3x+1 has a y-intercept of 1 and a slope of 3. This means that for every increase of 1 in the x-value, the y-value increases by 3.

The line y=2x+5 has a y-intercept of 5 and a slope of 2. This means that for every increase of 1 in the x-value, the y-value increases by 2.

To graph the lines, we can choose a few x-values and calculate the corresponding y-values.

For the line y=3x+1:
- When x=0, y=1.
- When x=1, y=4.
- When x=-1, y=-2.

For the line y=2x+5:
- When x=0, y=5.
- When x=1, y=7.
- When x=-1, y=3.

Using these points, we can plot the lines on a graph.

The first line, y=3x+1, passes through the points (0, 1), (1, 4), and (-1, -2).

The second line, y=2x+5, passes through the points (0, 5), (1, 7), and (-1, 3).

The point where the lines intersect is the solution to the simultaneous inequalities y>3x+1 and y≤2x+5.