2x² – xy - 15y2 How to factor by grouping
1 answer:
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Answer:
- The graph of this line i.e.
should be BELOW the DOTTED line as
involves < symbol.
- The graph of this line i.e.
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.
<em>Considering the line 1</em>
Solving line 1
As 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 is being shown ABOVE the SOLID line.
Therefore, the graph of this line i.e. should be BELOW the DOTTED line as it involves < symbol.
<em>Considering the line 2</em>
As 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 is being shown ABOVE the SOLID line.
Therefore, the graph of this line i.e. should be ABOVE the DOTTED line as it involves > symbol.
The <em>correct graph</em> for line 1 i.e. and line 2 i.e.
is shown in <em>attached figure</em>.
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.
<em>Solution Verification:</em>
<u><em>Putting (5, -2) in line 1 and line 2</em></u>
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
<em><u>Putting (-1, -1) in line 1 and line 2</u></em>
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
<em><u>Putting (0, 5) in line 1 and line 2</u></em>
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
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<em>Keywords: inequality, solution, graph, dotted line, solid line</em>
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