Question

Solve the system of inequalities: y + 2x > 3 and y Greater-than-or-equal-to 3.5x − 5 The first inequality, y + 2x > 3, is in slope-intercept form. The first inequality, y + 2x > 3, has a boundary line. The second inequality, y Greater-than-or-equal-to 3.5x − 5, has a boundary line. Both inequalities have a solution set that is shaded their boundary lines. is a point in the solution set of the system of inequalities.

Answer 1

Answer:

Here's what I get.

Step-by-step explanation:

1. Graphing the system of inequalities

The graph of y + 2x > 3 is in red. All points that satisfy this inequality are in the shaded red area.

The graph of y ≥ 3.5x - 5 is in blue. All points that satisfy this inequality are in the shaded blue area.

Both inequalities have a solution set in the purple shaded area above their boundary lines  

2. First inequality

The first inequality, y + 2x > 3, is not in slope-intercept form. The slope-intercept form would be y > -2x + 3.

It has a dashed boundary line to show that points in the line do not satisfy the inequality.

3. Second inequality

The second inequality, y ≥ 3.5x - 5, has a solid boundary line to show that points on it satisfy the inequality.

4. A point in the solution set

The point (1,2) is in the purple shaded solution area for the system. It satisfies both inequalities.  

$\begin{array}{rcl}y + 2x > 3 & \qquad & y \geq 3.5x - 5\\2 + 2(1) > 3 & \qquad & 2 \geq 3.5(1) - 5\\2 + 2 > 3 & \qquad & 2 \geq 3.5 - 5\\4 > 3 & \qquad & 2\geq -1.5 \\\textbf{TRUE} & \qquad &\textbf{TRUE}\\\end{array}$