Question

complète les systèmes dinéquations si lorigine appartient à la région-solution de chaque système dinéquations.
3x - 2y
5x + 4y
y
y
3x - 8
-2x + 6

Explanation:

To solve the system of linear inequalities, we first consider the origin \((0,0)\) and check which inequality it satisfies.

Step 1: Check the first inequality \(3x - 2y \square 5\)

Substitute \(x = 0\) and \(y = 0\) into \(3x - 2y\):
\[
3(0) - 2(0) = 0
\]
We compare \(0\) with \(5\). Since \(0 < 5\), the inequality for \(3x - 2y\) should be \(3x - 2y < 5\).

Step 2: Check the second inequality \(5x + 4y \square 8\)

Substitute \(x = 0\) and \(y = 0\) into \(5x + 4y\):
\[
5(0) + 4(0) = 0
\]
We compare \(0\) with \(8\). Since \(0 < 8\), the inequality for \(5x + 4y\) should be \(5x + 4y < 8\).

Step 3: Check the third inequality \(y \square 3x - 8\)

Substitute \(x = 0\) and \(y = 0\) into \(3x - 8\):
\[
3(0) - 8 = -8
\]
We compare \(0\) with \(-8\). Since \(0 > -8\), the inequality for \(y\) and \(3x - 8\) should be \(y > 3x - 8\).

Step 4: Check the fourth inequality \(y \square -2x + 6\)

Substitute \(x = 0\) and \(y = 0\) into \(-2x + 6\):
\[
-2(0) + 6 = 6
\]
We compare \(0\) with \(6\). Since \(0 < 6\), the inequality for \(y\) and \(-2x + 6\) should be \(y < -2x + 6\).

Final Answer

• \(3x - 2y < 5\)
• \(5x + 4y < 8\)
• \(y > 3x - 8\)
• \(y < -2x + 6\)

Answer:

To solve the system of linear inequalities, we first consider the origin \((0,0)\) and check which inequality it satisfies.

Step 1: Check the first inequality \(3x - 2y \square 5\)

Substitute \(x = 0\) and \(y = 0\) into \(3x - 2y\):
\[
3(0) - 2(0) = 0
\]
We compare \(0\) with \(5\). Since \(0 < 5\), the inequality for \(3x - 2y\) should be \(3x - 2y < 5\).

Step 2: Check the second inequality \(5x + 4y \square 8\)

Substitute \(x = 0\) and \(y = 0\) into \(5x + 4y\):
\[
5(0) + 4(0) = 0
\]
We compare \(0\) with \(8\). Since \(0 < 8\), the inequality for \(5x + 4y\) should be \(5x + 4y < 8\).

Step 3: Check the third inequality \(y \square 3x - 8\)

Substitute \(x = 0\) and \(y = 0\) into \(3x - 8\):
\[
3(0) - 8 = -8
\]
We compare \(0\) with \(-8\). Since \(0 > -8\), the inequality for \(y\) and \(3x - 8\) should be \(y > 3x - 8\).

Step 4: Check the fourth inequality \(y \square -2x + 6\)

Substitute \(x = 0\) and \(y = 0\) into \(-2x + 6\):
\[
-2(0) + 6 = 6
\]
We compare \(0\) with \(6\). Since \(0 < 6\), the inequality for \(y\) and \(-2x + 6\) should be \(y < -2x + 6\).

Final Answer

• \(3x - 2y < 5\)
• \(5x + 4y < 8\)
• \(y > 3x - 8\)
• \(y < -2x + 6\)