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Elan Coil [88]
1 year ago
14

To solve a system of inequalities so you can graph it how do you change these two equations into something like the two that are

on number one?Problem #2.

Mathematics
1 answer:
Zigmanuir [339]1 year ago
8 0
Explanation

Problem #2

We must find the solution to the following system of inequalities:

\begin{gathered} 3x-2y\leq4, \\ x+3y\leq6. \end{gathered}

(1) We solve for y the first inequality:

-2y\leq4-3x.

Now, we multiply both sides of the inequality by (-1), this changes the signs on both sides and inverts the inequality symbol:

\begin{gathered} 2y\ge-4+3x, \\ y\ge\frac{3}{2}x-2. \end{gathered}

The solution to this inequality is the set of all the points (x, y) over the line:

y=\frac{3}{2}x-2.

This line has:

• slope m = 3/2,

,

• y-intercept b = -2.

(2) We solve for y the second inequality:

\begin{gathered} x+3y\leq6, \\ 3y\leq6-x, \\ y\leq-\frac{1}{3}x+2. \end{gathered}

The solution to this inequality is the set of all the points (x, y) below the line:

y=-\frac{1}{3}x+2.

This line has:

• slope m = -1/3,

,

• y-intercept b = 2.

(3) Plotting the lines of points (1) and (2), and painting the region:

• over the line from point (1),

,

• and below the line from point (2),

we get the following graph:

Answer

The points that satisfy both inequalities are given by the intersection of the blue and red regions:

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