Question

what point is a solution to the linear inequality 4x - y ≤ 10

Answer 1

To find a point that satisfies the linear inequality \(4x - y \leq 10\), we can choose a specific value for \(x\) and then solve for \(y\).

Let's start by choosing \(x = 0\):

\[
4(0) - y \leq 10
\]
\[
-y \leq 10
\]
\[
y \geq -10
\]

So, one possible point that satisfies the inequality is \((0, -10)\).

Now, let's choose another value for \(x\). For \(x = 3\):

\[
4(3) - y \leq 10
\]
\[
12 - y \leq 10
\]
\[
-y \leq -2
\]
\[
y \geq 2
\]

So another point that satisfies the inequality could be \((3, 2)\).

Both points \((0, -10)\) and \((3, 2)\) are solutions to the inequality \(4x - y \leq 10\). There are infinitely many points that can satisfy this inequality!