18. Systems of Equations and Matrices

Graphing Systems of Inequalities

18. Systems of Equations and Matrices

Graphing Systems of Inequalities

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Multiple Choice

Graph the system of inequalities and indicate the region (if any) of solutions satisfying all equations.

$x+y\le4$
$y\ge1$ $x>0$

option a

option b

option c

option d

Verified step by step guidance

Start by graphing the inequality x + y ≤ 4. This can be rewritten as y ≤ -x + 4. The boundary line is y = -x + 4, which is a straight line with a slope of -1 and a y-intercept of 4. Shade the region below this line, as the inequality is less than or equal to.

Next, graph the inequality y ≥ 1. This is a horizontal line at y = 1. Shade the region above this line, as the inequality is greater than or equal to.

Now, graph the inequality x > 0. This is a vertical line at x = 0. Shade the region to the right of this line, as the inequality is greater than.

The solution to the system of inequalities is the region where all shaded areas overlap. This is the region that satisfies all three inequalities simultaneously.

Identify the region of overlap on the graph. This region should be bounded by the lines y = -x + 4, y = 1, and x = 0, and it should be in the first quadrant where x is positive.