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MrsStrong

Answer:

See picture attached.

Step-by-step explanation:

To find the solution, graph each equation using the y = mx + b form.

Start by converting to this form.

x + 2y < 4 becomes y < -1/2x +2

3x - y > 2 becomes y < 3x - 2

Then mark each y-intercept. These points are (0,2) and (0,-2).

Using the slope mark the next points at (-1,4) and (1, -1) respectively.

Connect using dash lines since this is not equal to in either inequality.

Test a point no on either line like (-1,-1).

If the inequality holds true, shade the area.

Where the areas overlap is the solution. See picture.

Ver imagen MrsStrong
MrRoyal

Inequalities are used to represent unequal expressions.

The solution to the inequality is [tex]x \le \frac 87[/tex] and [tex]y < \frac{10}7[/tex]

The inequalities are given as:

[tex]x + 2y \le 4[/tex]

[tex]3x - y > 2[/tex]

Express both inequalities as equations'

[tex]x + 2y = 4[/tex]

[tex]3x -y = 2[/tex]

Make y the subject in [tex]3x -y = 2[/tex]

[tex]y = 3x - 2[/tex]

Substitute [tex]y = 3x - 2[/tex] in [tex]x + 2y \le 4[/tex]

[tex]x + 2(3x - 2) \le 4[/tex]

Open brackets

[tex]x + 6x - 4 \le 4[/tex]

[tex]7x - 4 \le 4[/tex]

Collect like terms

[tex]7x \le 4+4[/tex]

[tex]7x \le 8[/tex]

Divide both sides by 7

[tex]x \le \frac 87[/tex]

Substitute 8/7 for x in [tex]3x - y > 2[/tex]

[tex]3 \times \frac 87 - y > 2[/tex]

[tex]\frac{24}7 - y > 2[/tex]

Collect like terms

[tex]- y > 2 -\frac{24}7[/tex]

Take LCM

[tex]- y > \frac{14 -24}7[/tex]

[tex]- y > \frac{-10}7[/tex]

Divide both sides by -1

[tex]y < \frac{10}7[/tex]

Read more about inequalities at:

https://brainly.com/question/15137133

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