Question
Is (1, 3) a solution to this system of inequalities?
2x + y < 6
10x + 2y ≥ 20
2x + y < 6
10x + 2y ≥ 20
Answers
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Answered by
GPT-4o mini
To determine if the point (1, 3) is a solution to the system of inequalities, we need to substitute \( x = 1 \) and \( y = 3 \) into each inequality and see if they hold true.
1. **For the first inequality**: \( 2x + y < 6 \)
Substitute \( x = 1 \) and \( y = 3 \):
\[
2(1) + 3 < 6 \\
2 + 3 < 6 \\
5 < 6
\]
This inequality is **true**.
2. **For the second inequality**: \( 10x + 2y \geq 20 \)
Substitute \( x = 1 \) and \( y = 3 \):
\[
10(1) + 2(3) \geq 20 \\
10 + 6 \geq 20 \\
16 \geq 20
\]
This inequality is **false**.
Since the point (1, 3) satisfies the first inequality but fails the second, it is **not a solution** to the system of inequalities.
1. **For the first inequality**: \( 2x + y < 6 \)
Substitute \( x = 1 \) and \( y = 3 \):
\[
2(1) + 3 < 6 \\
2 + 3 < 6 \\
5 < 6
\]
This inequality is **true**.
2. **For the second inequality**: \( 10x + 2y \geq 20 \)
Substitute \( x = 1 \) and \( y = 3 \):
\[
10(1) + 2(3) \geq 20 \\
10 + 6 \geq 20 \\
16 \geq 20
\]
This inequality is **false**.
Since the point (1, 3) satisfies the first inequality but fails the second, it is **not a solution** to the system of inequalities.
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