Question

1. which point is a solution to the system below?

$5x + 10y > -10$
$-2x - y \leq 7$

1. $(-4, 1)$
2. $(3, -3)$
3. $(-6, 5)$
4. $(0, -7)$

Explanation:

Step1: Test point (-4,1)

Substitute \(x = -4\), \(y = 1\) into \(5x + 10y > -10\):
\(5(-4)+10(1)= -20 + 10 = -10\). The inequality is \(> -10\), so \(-10 > -10\) is false.

Substitute into \(-2x - y \leq 7\):
\(-2(-4)-1 = 8 - 1 = 7\). \(7 \leq 7\) is true, but first inequality fails.

Step2: Test point (3, -3)

Substitute into \(5x + 10y > -10\):
\(5(3)+10(-3)=15 - 30 = -15\). \(-15 > -10\) is false.

Step3: Test point (-6, 5)

Substitute into \(5x + 10y > -10\):
\(5(-6)+10(5)= -30 + 50 = 20\). \(20 > -10\) is true.

Substitute into \(-2x - y \leq 7\):
\(-2(-6)-5 = 12 - 5 = 7\). \(7 \leq 7\) is true.

Step4: Test point (0, -7)

Substitute into \(5x + 10y > -10\):
\(5(0)+10(-7)= -70\). \(-70 > -10\) is false.

Answer:

1. \((-6, 5)\)