1Cademy - Solving $$\left\{x > -4,\; x - 2y \geq -4\right\}$$ by Graphing

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Solving a System of Linear Inequalities by Graphing

Example

Solving $\left\{x > -4,\; x - 2y \geq -4\right\}$ by Graphing

Solve the system $\left\{\begin{array}{l} x > -4 \\ x - 2y \geq -4 \end{array}\right.$ by graphing.

Step 1 — Graph $x > -4$ . The boundary line is $x = -4$ , a vertical line passing through $x = -4$ . Because the inequality uses $>$ (strict), draw a dashed line. Test $(0, 0)$ : $0 > -4$ is true, so shade the side that contains the origin.

Step 2 — Graph $x - 2y \geq -4$ on the same grid. The boundary line is $x - 2y = -4$ , which has intercepts $x = -4$ and $y = 2$ . Because the inequality uses $\geq$ (non-strict), draw a solid line. Test $(0, 0)$ : $0 - 2(0) \geq -4$ gives $0 \geq -4$ , which is true, so shade the side that contains the origin.

Step 3 — Identify the solution. The solution is the overlapping shaded region. The intersection point of the boundary lines is not included because one boundary line is dashed.

Step 4 — Verify with a test point. Choose a test point in the overlapping region and substitute it into both inequalities to confirm both are true.

Updated 2026-05-25

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OpenStax Intermediate Algebra

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