Two-variable linear inequalities Calculator

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Example

Created on 2024-06-20Asked by Theodore Miller (Solvelet student)

Graph the system of inequalities:

\begin{cases} 2x + 3y \leq 6 \\ 4x - y > 5 \end{cases}

Solution

\ To graph the system of inequalities:

\begin{cases} 2x + 3y \leq 6 \\ 4x - y > 5 \end{cases}

1. **Graph the boundary lines:** - For

2x + 3y = 6

: -

y = 0 \implies x = 3

x = 0 \implies y = 2

- For

4x - y = 5

: -

y = 0 \implies x = \frac{5}{4}

x = 0 \implies y = -5

2. **Plot the boundary lines and test points to determine the shaded regions:** \begin{tikzpicture} \begin{axis}[ axis lines = middle, xlabel = {

x

}, ylabel = {

y

}, xmin = -1, xmax = 4, ymin = -2, ymax = 3, grid = major, legend pos = outer north east, ] \addplot [ domain=0:3, samples=100, color=blue, ] {(6 - 2*x)/3}; \addlegendentry{

2x + 3y = 6

} \addplot [ domain=1:3, samples=100, color=red, ] {4*x - 5}; \addlegendentry{

4x - y = 5

} \end{axis} \end{tikzpicture} 3. **Shade the regions:** - For

2x + 3y \leq 6

, shade below and on the line. - For

4x - y > 5

, shade above the line. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Penelope Miller on Solvelet

1. Graph the solution set for the inequality

y < 2x - 1

on the coordinate plane.2. Determine the solution set for the inequality

3y + 2x \leq 6

DefinitionA Two-variable linear inequality is a real-valued relation that holds when two mathematical expressions are compared with respect to two variables Being more specific, a Two-variable linear inequality has the following form ax+by≤c ax+by ≥ c ax+byx where the solution is a set of regions in the xy-plane that satisfies the inequality. This would be written as the inequality x+2y≤4, which describes the area under the line x+2y=4. Two-variable

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