1Cademy - Checking Whether $$(-2, 1)$$ and $$(4, -1)$$ are Solutions of $$\{y > 4x - 2,\; 4x

Activity (Process)

Checking Whether $(-2, 1)$ and $(4, -1)$ are Solutions of $\{y > 4x - 2,\; 4x - y < 20\}$

Determine whether each ordered pair is a solution to the system $\left\{\begin{array}{l} y > 4x - 2 \\ 4x - y < 20 \end{array}\right.$

ⓐ Testing $(-2, 1)$ : Substitute $x = -2$ and $y = 1$ into both inequalities.

First inequality: $1 > 4(-2) - 2 \implies 1 > -8 - 2 \implies 1 > -10$ . Since $1 > -10$ is true, the first inequality is satisfied.
Second inequality: $4(-2) - 1 < 20 \implies -8 - 1 < 20 \implies -9 < 20$ . Since $-9 < 20$ is true, the second inequality is also satisfied.

Because $(-2, 1)$ makes both inequalities true, it is a solution to the system.

ⓑ Testing $(4, -1)$ : Substitute $x = 4$ and $y = -1$ into both inequalities.

First inequality: $-1 > 4(4) - 2 \implies -1 > 16 - 2 \implies -1 > 14$ . Since $-1 > 14$ is false, the first inequality is not satisfied.
Second inequality: $4(4) - (-1) < 20 \implies 16 + 1 < 20 \implies 17 < 20$ . Since $17 < 20$ is true, the second inequality is satisfied.

Because $(4, -1)$ fails to satisfy the first inequality, it is not a solution to the system.

Updated 2026-05-26

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