Question

Line 1: 2x-3y>12

Answer 1

Answer:

• The graph of this line i.e. $2x-3y>12$ should be BELOW the DOTTED line as $y$ involves < symbol.
• The graph of this line i.e. $y>-2x+5$  should be ABOVE the DOTTED line as it involves > symbol.
• The correct graph for line 1  and line 2 is shown in attached figure.

Step-by-step explanation:

• If the inequality involves < or >, then the graph of the equation involves a dotted line.  
• If the inequality involves ≤ or ≥, then the graph of the equation involves a solid line.

Considering the line 1

$2x-3y>12$

Solving line 1

$2x-3y>12$

$-3y>12-2x$

$3y$

$y$

As $y$ involves < symbol, so the graph of this line should be BELOW the DOTTED line.

But, as you can see that there is an error in the graph. As the graph of  $y$ is being shown ABOVE the SOLID line.

Therefore, the graph of this line i.e. $y$ should be BELOW the DOTTED line as it involves < symbol.

Considering the line 2

$y>-2x+5$

As $y>-2x+5$ involves > symbol, so the graph of this line should be ABOVE the DOTTED line.

But, as you can see that there is an error in the graph. As the graph of  $y>-2x+5$ is being shown ABOVE the SOLID line.

Therefore, the graph of this line i.e. $y>-2x+5$ should be ABOVE the DOTTED line as it involves > symbol.

The correct graph for line 1 i.e. $2x-3y>12$ and line 2 i.e. $y>-2x+5$ is shown in attached figure.

From the attached graph, it is shown that only (5, -2) satisfies the both inequalities. So, (5, -2) is the correct solution for the given inequalities.

Solution Verification:

Putting (5, -2) in line 1 and line 2

For line 1:

2x - 3y > 12 ⇒ 2(5) - 3(-2) > 12 ⇒ 10 + 6 > 12 ⇒ 16 > 12 which is true.

For line 2:

y > -2x + 5 ⇒ -2 > -2(5) + 5 ⇒ -2 > -10 + 5 ⇒ -2 > -5 which is true.

So, (5, -2) is IN the solution for line 1 and line 2

Putting (-1, -1) in line 1 and line 2

For line 1:

2x - 3y > 12 ⇒ 2(-1) - 3(-1) > 12 ⇒ -2 + 3 > 12 ⇒ 1 > 12 which is false.

For line 2:

y > -2x + 5 ⇒ -1 > -2(-1) + 5 ⇒ -1 > 2 + 5 ⇒ -1 > 7 which is false.

So, (-1, -1) is NOT in the solution for line 1 and line 2

Putting (0, 5) in line 1 and line 2

For line 1:

2x - 3y > 12 ⇒ 2(0) - 3(5) > 12 ⇒ 0 - 15 > 12 ⇒ -15 > 12 which is false.

For line 2:

y > -2x + 5 ⇒ 5 > -2(0) + 5 ⇒ 5 > 0 + 5 ⇒ 5 > 5 which is false.

So, (0, 5) is NOT in the solution for line 1 and line 2

Keywords: inequality, solution, graph, dotted line, solid line

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